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 has a fixed cost of $26,000 / month when it is producing printed tapestries. Each item that it makes has its own cost of $34. One month the company filled an order for 2400 of its tapestries, selling each item for $63. How much profit was generated by the order? [U]Set up Cost function C(t) where t is the number of tapestries:[/U] C(t) = Cost per tapestry * number of tapestries + Fixed Cost C(t) = 34t + 26000 [U]Set up Revenue function R(t) where t is the number of tapestries:[/U] R(t) = Sale Price * number of tapestries R(t) = 63t [U]Set up Profit function P(t) where t is the number of tapestries:[/U] P(t) = R(t) - C(t) P(t) = 63t - (34t + 26000) P(t) = 63t - 34t - 26000 P(t) = 29t - 26000 [U]The problem asks for profit when t = 2400:[/U] P(2400) = 29(2400) - 26000 P(2400) = 69,600 - 26,000 P(2400) = [B]43,600[/B]

A company has a fixed cost of $34,000 and a production cost of $6 for each unit it manufactures. A unit sells for $15 Set up the cost function C(u) where u is the number of units is: C(u) = Cost per unit * u + Fixed Cost C(u) = [B]6u + 34000[/B] Set up the revenue function R(u) where u is the number of units is: R(u) = Sale price per unit * u R(u) = [B]15u[/B]

A company is planning to manufacture a certain product. The fixed costs will be $474778 and it will cost $293 to produce each product. Each will be sold for $820. Find a linear function for the profit, P , in terms of units sold, x . [U]Set up the cost function C(x):[/U] C(x) = Cost per product * x + Fixed Costs C(x) = 293x + 474778 [U]Set up the Revenue function R(x):[/U] R(x) = Sale Price * x R(x) = 820x [U]Set up the Profit Function P(x):[/U] P(x) = Revenue - Cost P(x) = R(x) - C(x) P(x) = 820x - (293x + 474778) P(x) = 820x - 293x - 474778 [B]P(x) = 527x - 474778[/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 specializes in personalized team uniforms. It costs the company $15 to make each uniform along with their fixed costs at $640. The company plans to sell each uniform for $55. [U]The cost function for "u" uniforms C(u) is given by:[/U] C(u) = Cost per uniform * u + Fixed Costs [B]C(u) = 15u + 640[/B] Build the revenue function R(u) where u is the number of uniforms: R(u) = Sale Price per uniform * u [B]R(u) = 55u[/B] Calculate break even function: Break even is where Revenue equals cost C(u) = R(u) 15u + 640 = 55u To solve for u, we [URL='https://www.mathcelebrity.com/1unk.php?num=15u%2B640%3D55u&pl=Solve']type this equation into our search engine[/URL] and we get: u = [B]16 So we break even selling 16 uniforms[/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 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 $12 for each unit produced. The product sells for $20/unit [U]Cost Function C(u) where u is the number of units:[/U] C(u) = cost per unit * u + fixed cost C(u) = 12u + 100000 [U]Revenue Function R(u) where u is the number of units:[/U] R(u) = Sale price * u R(u) = 20u Break even point is where C(u) = R(u): C(u) = R(u) 12u + 100000 = 20u To solve for u, we [URL='https://www.mathcelebrity.com/1unk.php?num=12u%2B100000%3D20u&pl=Solve']type this equation into our search engine[/URL] and we get: u = [B]12,500[/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 manufacturer has a monthly fixed cost of $25,500 and a production cost of $7 for each unit produced. The product sells for $10/unit. Set up cost function where u equals each unit produced: C(u) = 7u + 25,500 Set up revenue function R(u) = 10u Break Even is where Cost equals Revenue 7u + 25,500 = 10u Plug this into our [URL='http://www.mathcelebrity.com/1unk.php?num=7u%2B25500%3D10u&pl=Solve']equation calculator[/URL] to get [B]u = 8,500[/B]

A manufacturer has a monthly fixed cost of $52,500 and a production cost of $8 for each unit produced. The product sells for $13/unit. Using our [URL='http://www.mathcelebrity.com/cost-revenue-profit-calculator.php?fc=52500&vc=8&r=13&u=20000%2C50000&pl=Calculate']cost-revenue-profit calculator[/URL], we get the following: [LIST] [*]P(x) = 55x - 2,500 [*]P(20,000) = 47,500 [*]P(50,000) = 197,500 [/LIST]

A pretzel factory has daily fixed costs of $1100. In addition, it costs 70 cents to produce each bag of pretzels. A bag of pretzels sells for $1.80. [U]Build the cost function C(b) where b is the number of bags of pretzels:[/U] C(b) = Cost per bag * b + Fixed Costs C(b) = 0.70b + 1100 [U]Build the revenue function R(b) where b is the number of bags of pretzels:[/U] R(b) = Sale price * b R(b) = 1.80b [U]Build the revenue function P(b) where b is the number of bags of pretzels:[/U] P(b) = Revenue - Cost P(b) = R(b) - C(b) P(b) = 1.80b - (0.70b + 1100) P(b) = 1.80b = 0.70b - 1100 P(b) = 1.10b - 1100

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]

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

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]

Free Earnings Before Interest and Taxes (EBIT) and Net Income Calculator - Given inputs of sales, fixed costs, variable costs, depreciation, and taxes, this will determine EBIT and Net Income and Profit Margin

fixed cost 500 marginal cost 8 item sells for 30. Set up Cost Function C(x) where x is the number of items sold: C(x) = Marginal Cost * x + Fixed Cost C(x) = 8x + 500 Set up Revenue Function R(x) where x is the number of items sold: R(x) = Revenue per item * items sold R(x) = 30x Set up break even function (Cost Equals Revenue) C(x) = R(x) 8x + 500 = 30x Subtract 8x from each side: 22x = 500 Divide each side by 22: x = 22.727272 ~ 23 units for breakeven

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]

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].

Larry is buying new clothes for his return to school. He is buying shoes for $57 and shirts cost $15 each. He has $105 to spend. Which of the following can be solved to find the number of shirts he can afford? Let s be the number of shirts. Since shoes are a one-time fixed cost, we have: 15s + 57 = 105 We want to solve this equation for s. We [URL='https://www.mathcelebrity.com/1unk.php?num=15s%2B57%3D105&pl=Solve']type it in our math engine[/URL] and we get: s = [B]3.2 or 3 whole shirts[/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]

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 of x ice cream if one ice cream cost $9 and the fixed cost is $8142 Cost function is C(x) is: C(x) = Cost per ice cream * number of ice creams + Fixed Cost C(x) = [B]9x + 8142[/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 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 cost are $2500 and the cost per unit $20 Total Cost = Cost per Unit * Units + Fixed Cost Total Cost = [B]20x + 2500[/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 have $20 to spend on a taxi fare. The ride costs $5 plus $2.50 per kilometer. Let k be the number of kilometers. Total Cost = Cost per kilometer * number of kilometers + Fixed Cost With k for kilometers, 2.5 as cost per kilometer, and 5 as fixed cost, and 20 on total cost, we have: 2.5k + 5 = 20 To solve this equation for k, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.5k%2B5%3D20&pl=Solve']type it in our math engine [/URL]and we get k = [B]6[/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]