A bakery has a fixed cost of $119.75 per a day plus $2.25 for each pastry. The bakery would like to keep its daily costs at or below $500 per day. Which inequality shows the maximum number of pastries, p, that can be baked each day. Set up the cost function C(p), where p is the number of pastries: C(p) = Variable Cost + Fixed Cost C(p) = 2.25p + 119.75 The problem asks for C(p) at or below $500 per day. The phrase [I]at or below[/I] means less than or equal to (<=). [B]2.25p + 119.75 <= 500[/B]

a bicycle store costs $3600 per month to operate. The store pays an average of $60 per bike. the average selling price of each bicycle is $100. how many bicycles must the store sell each month to break even? Cost function C(b) where b is the number of bikes: C(b) = Variable Cost + Fixed Cost C(b) = Cost per bike * b + operating cost C(b) = 60b + 3600 Revenue function R(b) where b is the number of bikes: R(b) = Sale price * b R(b) = 100b Break Even is when Cost equals Revenue, so we set C(b) = R(b): 60b + 3600 = 100b To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=60b%2B3600%3D100b&pl=Solve']type it in our math engine[/URL] and we get: b = [B]90[/B]

A book publishing company has fixed costs of $180,000 and a variable cost of $25 per book. The books they make sell for $40 each. [B][U]Set up Cost Function C(b) where b is the number of books:[/U][/B] C(b) = Fixed Cost + Variable Cost x Number of Units C(b) = 180,000 + 25(b) [B]Set up Revenue Function R(b):[/B] R(b) = 40b Set them equal to each other 180,000 + 25b = 40b Subtract 25b from each side: 15b = 180,000 Divide each side by 15 [B]b = 12,000 for break even[/B]

A company makes toy boats. Their monthly fixed costs are $1500. The variable costs are $50 per boat. They sell boats for $75 a piece. How many boats must be sold each month to break even? [U]Set up Cost function C(b) where t is the number of tapestries:[/U] C(b) = Cost per boat * number of boats + Fixed Cost C(b) = 50b + 1500 [U]Set up Revenue function R(b) where t is the number of tapestries:[/U] R(b) = Sale Price * number of boats R(b) = 75b [U]Break even is where Revenue equals Cost, or Revenue minus Cost is 0, so we have:[/U] R(b) - C(b) = 0 75b - (50b + 1500) = 0 75b - 50b - 1500 = 0 25b - 1500 = 0 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=25b-1500%3D0&pl=Solve']type this equation in our math engine[/URL] and we get: b = [B]60[/B]

A company that manufactures lamps has a fixed monthly cost of $1800. It costs $90 to produce each lamp, and the selling price is $150 per lamp. Set up the Cost Equation C(l) where l is the price of each lamp: C(l) = Variable Cost x l + Fixed Cost C(l) = 90l + 1800 Determine the revenue function R(l) R(l) = 150l Determine the profit function P(l) Profit = Revenue - Cost P(l) = 150l - (90l + 1800) P(l) = 150l - 90l - 1800 [B]P(l) = 60l - 1800[/B] Determine the break even point: Breakeven --> R(l) = C(l) 150l = 90l + 1800 [URL='https://www.mathcelebrity.com/1unk.php?num=150l%3D90l%2B1800&pl=Solve']Type this into the search engine[/URL], and we get [B]l = 30[/B]

A corn refining company produces corn gluten cattle feed at a variable cost of $84 per ton. If fixed costs are $110,000 per month and the feed sells for $132 per ton, how many tons should be sold each month to have a monthly profit of $560,000? [U]Set up the cost function C(t) where t is the number of tons of cattle feed:[/U] C(t) = Variable Cost * t + Fixed Costs C(t) = 84t + 110000 [U]Set up the revenue function R(t) where t is the number of tons of cattle feed:[/U] R(t) = Sale Price * t R(t) = 132t [U]Set up the profit function P(t) where t is the number of tons of cattle feed:[/U] P(t) = R(t) - C(t) P(t) = 132t - (84t + 110000) P(t) = 132t - 84t - 110000 P(t) = 48t - 110000 [U]The question asks for how many tons (t) need to be sold each month to have a monthly profit of 560,000. So we set P(t) = 560000:[/U] 48t - 110000 = 560000 [U]To solve for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=48t-110000%3D560000&pl=Solve']type this equation into our search engine[/URL] and we get:[/U] t =[B] 13,958.33 If the problem asks for whole numbers, we round up one ton to get 13,959[/B]

A gym membership has a $50 joining fee plus charges $17 a month for m months Build a cost equation C(m) where m is the number of months of membership. C(m) = Variable Cost * variable units + Fixed Cost C(m) = Months of membership * m + Joining Fee Plugging in our numbers and we get: [B]C(m) = 17m + 50 [MEDIA=youtube]VGXeqd3ikAI[/MEDIA][/B]

A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children. What was the cost of each ticket? Declare variables: [LIST] [*]Let a be the number of adult's tickets [*]Let c be the number of children's tickets [/LIST] Cost = Price * Quantity We're given two equations: [LIST=1] [*]a + c = 20 [*]15a + 10c = 225 [/LIST] Rearrange equation (1) in terms of a: [LIST=1] [*]a = 20 - c [*]15a + 10c = 225 [/LIST] Now that I have equation (1) in terms of a, we can substitute into equation (2) for a: 15(20 - c) + 10c = 225 Solve for [I]c[/I] in the equation 15(20 - c) + 10c = 225 We first need to simplify the expression removing parentheses Simplify 15(20 - c): Distribute the 15 to each term in (20-c) 15 * 20 = (15 * 20) = 300 15 * -c = (15 * -1)c = -15c Our Total expanded term is 300-15c Our updated term to work with is 300 - 15c + 10c = 225 We first need to simplify the expression removing parentheses Our updated term to work with is 300 - 15c + 10c = 225 [SIZE=5][B]Step 1: Group the c terms on the left hand side:[/B][/SIZE] (-15 + 10)c = -5c [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] -5c + 300 = + 225 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 300 and 225. To do that, we subtract 300 from both sides -5c + 300 - 300 = 225 - 300 [SIZE=5][B]Step 4: Cancel 300 on the left side:[/B][/SIZE] -5c = -75 [SIZE=5][B]Step 5: Divide each side of the equation by -5[/B][/SIZE] -5c/-5 = -75/-5 c = [B]15[/B] Recall from equation (1) that a = 20 - c. So we substitute c = 15 into this equation to solve for a: a = 20 - 15 a = [B]5[/B]

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $10 for each unit produced. The product sells for $22/unit. The cost function for each unit u is: C(u) = Variable Cost * Units + Fixed Cost C(u) = 10u + 100000 The revenue function R(u) is: R(u) = 22u We want the break-even point, which is where: C(u) = R(u) 10u + 100000 = 22u [URL='https://www.mathcelebrity.com/1unk.php?num=10u%2B100000%3D22u&pl=Solve']Typing this equation into our search engine[/URL], we get: u =[B]8333.33[/B]

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $14 for each unit produced. The product sells for $20/unit. Let u be the number of units. We have a cost function C(u) as: C(u) = Variable cost * u + Fixed Cost C(u) = 14u + 100000 [U]We have a revenue function R(u) with u units as:[/U] R(u) = Sale Price * u R(u) = 20u [U]We have a profit function P(u) with u units as:[/U] Profit = Revenue - Cost P(u) = R(u) - C(u) P(u) = 20u - (14u + 100000) P(u) = 20u - 14u - 100000 P(u) = 6u - 1000000

A peanut vendor has initial start up costs of $7600 and variable costs of $0.70 per bag of peanuts. What is the cost function? We set up the cost function C(b) where b is the number of bags: C(b) = Cost per bag * b + Start up costs Plugging in our numbers, we get: [B]C(b) = 0.70b + 7600[/B]

A tire repair shop charges $5 for tool cost and $2 for every minute the worker spends on the repair. A) Write an equation of the total cost of repair, $y, in terms of a total of x minutes of repair. y = Variable Cost + Fixed Cost y = Cost per minute of repair * minutes of repair + Tool Cost [B]y = 2x + 5[/B]

Barbra is buying plants for her garden. She notes that potato plants cost $3 each and corn plants cost $4 each. If she plans to spend at least $20 and purchase less than 15 plants in total, create a system of equations or inequalities that model the situation. Define the variables you use. [U]Define variables[/U] [LIST] [*]Let c be the number of corn plants [*]Let p be the number of potato plants [/LIST] Since cost = price * quantity, we're given two inequalities: [LIST=1] [*][B]3p + 4c >= 20 (the phrase [I]at least[/I] means greater than or equal to)[/B] [*][B]c + p < 15[/B] [/LIST]

Free Break Even Calculator - Given a fixed cost, variable cost, and revenue function or value, this calculates the break-even point

Free Cost Revenue Profit Calculator - Given a total cost, variable cost, revenue amount, and profit unit measurement, this calculates profit for each profit unit

Dotty McGinnis starts up a small business manufacturing bobble-head figures of famous soccer players. Her initial cost is $3300. Each figure costs $4.50 to make. a. Write a cost function, C(x), where x represents the number of figures manufactured. Cost function is the fixed cost plus units * variable cost. [B]C(x) = 3300 + 4.50x[/B]

Dunder Mifflin will print business cards for $0.10 each plus setup charge of $15. Werham Hogg offers business cards for $0.15 each with a setup charge of $10. What numbers of business cards cost the same from either company Declare variables: [LIST] [*]Let b be the number of business cards. [/LIST] [U]Set up the cost function C(b) for Dunder Mifflin:[/U] C(b) = Cost to print each business card * b + Setup Charge C(b) = 0.1b + 15 [U]Set up the cost function C(b) for Werham Hogg:[/U] C(b) = Cost to print each business card * b + Setup Charge C(b) = 0.15b + 10 The phrase [I]cost the same[/I] means we set both C(b)'s equal to each other and solve for b: 0.1b + 15 = 0.15b + 10 Solve for [I]b[/I] in the equation 0.1b + 15 = 0.15b + 10 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 0.1b and 0.15b. To do that, we subtract 0.15b from both sides 0.1b + 15 - 0.15b = 0.15b + 10 - 0.15b [SIZE=5][B]Step 2: Cancel 0.15b on the right side:[/B][/SIZE] -0.05b + 15 = 10 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 15 and 10. To do that, we subtract 15 from both sides -0.05b + 15 - 15 = 10 - 15 [SIZE=5][B]Step 4: Cancel 15 on the left side:[/B][/SIZE] -0.05b = -5 [SIZE=5][B]Step 5: Divide each side of the equation by -0.05[/B][/SIZE] -0.05b/-0.05 = -5/-0.05 b = [B]100[/B]

Each piece of candy costs 25 cents. The cost of x pieces of candy is $2.00. Use variable x to translate the above statements into algebraic equation. Our algebraic expression is: [B]0.25x = 2 [/B] To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.25x%3D2&pl=Solve']type it in our search engine[/URL] and we get: x = [B]8[/B]

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Frank is a plumber who charges a $35 service charge and $15 per hour for his plumbing services. Find a linear function that expresses the total cost C for plumbing services for h hours. Cost functions include a flat rate and a variable rate. The flat rate is $35 and the variable rate per hour is 15. The cost function C(h) where h is the number of hours Frank works is: [B]C(h) = 15h + 35[/B]

Georgie joins a gym. she pays $25 to sign up and then $15 each month. Create an equation using this information. Let m be the number of months Georgie uses the gym. Our equation G(m) is the cost Georgie pays for m months. G(m) = Variable Cost * m (months) + Fixed Cost Plug in our numbers: [B]G(m) = 15m + 25[/B]

Happy Paws charges $16.00 plus $1.50 per hour to keep a dog during the day. Woof Watchers charges $11.00 plus $2.75 per hour. Complete the equation and solve it to find for how many hours the total cost of the services is equal. Use the variable h to represent the number of hours. Happy Paws Cost: C = 16 + 1.5h Woof Watchers: C = 11 + 2.75h Setup the equation where there costs are equal 16 + 1.5h = 11 + 2.75h Subtract 11 from each side: 5 + 1.5h = 2.75h Subtract 1.5h from each side 1.25h = 5 Divide each side by 1.25 [B]h = 4[/B]

Happy Paws charges $19.00 plus $5.50 per hour to keep a dog during the day. Woof Watchers charges $11.00 plus $6.75 per hour. Complete the equation and solve it to find for how many hours the total cost of the services is equal. Use the variable h to represent the number of hours. [B]Happy Paws cost equation:[/B] 5.50h + 19 [B]Woof Watchers cost equation:[/B] 6.75h + 11 [B]Set them equal to each other:[/B] 5.50h + 19 = 6.75h + 11 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=5.50h%2B19%3D6.75h%2B11&pl=Solve']equation solver[/URL], we get [B]h = 6.4[/B].

Free High and Low Method Calculator - Calculates the variable cost per unit, total fixed costs, and the cost volume formula

Free High-Low Method Calculator - Calculates Variable Cost per Unit, Total Fixed Cost, and Cost Volume using the High-Low Method

it costs $75.00 for a service call from shearin heating and air conditioning company. the charge for labor is $60.00 . how many full hours can they work on my air conditioning unit and still stay within my budget of $300.00 for repairs and service? Our Cost Function is C(h), where h is the number of labor hours. We have: C(h) = Variable Cost * Hours + Fixed Cost C(h) = 60h + 75 Set C(h) = $300 60h + 75 = 300 [URL='https://www.mathcelebrity.com/1unk.php?num=60h%2B75%3D300&pl=Solve']Running this problem in the search engine[/URL], we get [B]h = 3.75[/B].

Melissa runs a landscaping business. She has equipment and fuel expenses of $264 per month. If she charges $53 for each lawn, how many lawns must she service to make a profit of at $800 a month? Melissa has a fixed cost of $264 per month in fuel. No variable cost is given. Our cost function is: C(x) = Fixed Cost + Variable Cost. With variable cost of 0, we have: C(x) = 264 The revenue per lawn is 53. So R(x) = 53x where x is the number of lawns. Now, profit is Revenue - Cost. Our profit function is: P(x) = 53x - 264 To make a profit of $800 per month, we set P(x) = 800. 53x - 264 = 800 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=53x-264%3D800&pl=Solve']equation solver[/URL], we get: [B]x ~ 21 lawns[/B]

Mr. Chris’s new app “Tick-Tock” is the hottest thing to hit the app store since...ever. It costs $5 to buy the app and then $2.99 for each month that you subscribe (a bargain!). How much would it cost to use the app for one year? Write an equation to model this using the variable “m” to represent the number of months that you use the app. Set up the cost function C(m) where m is the number of months you subscribe: C(m) = Monthly Subscription Fee * months + Purchase fee [B]C(m) = 2.99m + 5[/B]

Sam purchased n notebooks. They were 4 dollars each. Write an equation to represent the total cost c that Sam paid. Cost Function is: [B]c = 4n[/B] Or, using n as a function variable, we write: c(n) = 4n

Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 cents of additional expense for each soda can made. Assuming all soda cans manufactured can be sold, find the break-even point. Calculate the revenue function R(c) where s is the number of sodas sold: R(s) = Sale Price * number of units sold R(s) = 50s Calculate the cost function C(s) where s is the number of sodas sold: C(s) = Variable Cost * s + Fixed Cost C(s) = 0.25s + 900 Our break-even point is found by setting R(s) = C(s): 0.25s + 900 = 50s We [URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B900%3D50s&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]18.09[/B]

The cost of having a plumber spend h hours at your house if the plumber charges $60 for coming to the house and $70 per hour labor: We have a fixed cost of $60 plus the variable cost of $70h. We add both for our total cost C(h): [B]C(h) = $70h + 60[/B]

The cost to rent a boat is $10. There is also charge of $2 for each person. Which expresion represents the total cost to rent a boat for p persons? The cost function includes a fixed cost of $10 plus a variable cost of 2 persons for p persons: [B]C(p) = 2p + 10[/B]

The fixed costs to produce a certain product are 15,000 and the variable costs are $12.00 per item. The revenue for a certain product is $27.00 each. If the company sells x products, then what is the revenue equation? R(x) = Revenue per item x number of products sold [B]R(x) = 27x[/B]

The phone company charges Rachel 12 cents per minute for her long distance calls. A discount company called Rachel and offered her long distance service for 1/2 cent per minute, but will charge a $46 monthly fee. How many minutes per month must Rachel talk on the phone to make the discount a better deal? Minutes Rachel talks = m Current plan cost = 0.12m New plan cost = 0.005m + 46 Set new plan equal to current plan: 0.005m + 46 = 0.12m Solve for [I]m[/I] in the equation 0.005m + 46 = 0.12m [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 0.005m and 0.12m. To do that, we subtract 0.12m from both sides 0.005m + 46 - 0.12m = 0.12m - 0.12m [SIZE=5][B]Step 2: Cancel 0.12m on the right side:[/B][/SIZE] -0.115m + 46 = 0 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 46 and 0. To do that, we subtract 46 from both sides -0.115m + 46 - 46 = 0 - 46 [SIZE=5][B]Step 4: Cancel 46 on the left side:[/B][/SIZE] -0.115m = -46 [SIZE=5][B]Step 5: Divide each side of the equation by -0.115[/B][/SIZE] -0.115m/-0.115 = -46/-0.115 m = [B]400 She must talk over 400 minutes for the new plan to be a better deal [URL='https://www.mathcelebrity.com/1unk.php?num=0.005m%2B46%3D0.12m&pl=Solve']Source[/URL][/B]

The total cost for 9 bracelets, including shipping was $72. The shipping charge was $9. Define your variable and write an equation that models the cost of each bracelet. We set up a cost function as fixed cost plus total cost. Fixed cost is the shipping charge of $9. So we have the following cost function where n is the cost of the bracelets: C(b) = nb + 9 We are given C(9) = 72 and b = 9 9n + 9 = 72 [URL='https://www.mathcelebrity.com/1unk.php?num=9n%2B9%3D72&pl=Solve']Run this through our equation calculator[/URL], and we get [B]n = 7[/B].

The total cost of producing x units for which the fixed costs are $2900 and the cost per unit is $25 [U]Set up the cost function:[/U] Cost function = Fixed Cost + Variable Cost per Unit * Number of Units [U]Plug in Fixed Cost = 2900 and Cost per Unit = $25[/U] [B]C(x) = 2900 + 25x [MEDIA=youtube]77PiD-VADjM[/MEDIA][/B]

You are buying boxes of cookies at a bakery. Each box of cookies costs $4. In the equation below, c represents the number of boxes of cookies you buy, and d represents the amount the cookies will cost you (in dollars). The relationship between these two variables can be expressed by the following equation: d=4c. Identify the dependent and independent variables. [B]The variable d is dependent, and c is independent since the value of d is determined by c.[/B]

You work for a remote manufacturing plant and have been asked to provide some data about the cost of specific amounts of remote each remote, r, costs $3 to make, in addition to $2000 for labor. Write an expression to represent the total cost of manufacturing a remote. Then, use the expression to answer the following question. What is the cost of producing 2000 remote controls? We've got 2 questions here. Question 1: We want the cost function C(r) where r is the number of remotes: C(r) = Variable Cost per unit * r units + Fixed Cost (labor) [B]C(r) = 3r + 2000 [/B] Question 2: What is the cost of producing 2000 remote controls. In this case, r = 2000, so we want C(2000) C(2000) = 3(2000) + 2000 C(2000) = 6000 + 2000 C(2000) = [B]$8000[/B]