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Linear cost and revenue equations are shown below. Find the break-even quantity.
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- The cost function for flavored coffee at an upscale coffeehouse is given in dollars by C(x) = 3x + 160, where x is in pounds. The coffee sells for $7 per pound.(a) Find the break-even quantity.(b) What will the revenue be at that point?A company makes solar panels. The company's revenue function, in dollars, is R(n) =10n, where n is the number of panels produced. The cost function is C(n) 100 (2)30. R and C are shown on the graph below. 1000 800 600 400 200 1 20 40 60 80 100 in Number of Panels a) Estimate from the graph i) the break-even points ii) the number of panels that should be produced for maximum profit b) Write the equation for the profit function P. c) Graph P. d) Use your graph of P to estimate the number of panels that give maximum profit. e) How would your answers for break-even points and maximum profit change if ) the number of dollars of revenue per panel is increased slightly? ii) the cost function is changed to C(n) 100(2)35? f) What does the number that was changed in part e) ii) represent?| %3D DollarsA company manufactures and sells book-cases .The selling price is $54.90 per book case.The total cost.The total cost function is linear, and cost amounts to $50,000 for 2,000 book-cases and $32,120 for 800 book-cases. (a)Write the equation for revenue.(b)Write the equation for total cost. (c)Find the break even point.
- The revenue and cost functions for a particular product are given below. The cost and revenue are given in dollars, and xrepresents the number of units . R(x) = −0.2x2 + 172x C(x) = 90x + 8385 e) what is the maximum profit?Use the equations for the total cost C and total revenue R to find the number x of units a company must sell to break even. (Round to the nearest whole unit.) C = 8950x + 220,000, R = 9857xA company makes solar panels. The company's revenue function, in dollars, is R(n)= 10n , where n is the number of panels produced. The cost function is C(n) = 100(2)30 . R and C are shown on the graph below. 1000 800 600 400 200 20 40 60 80 100 1 Number of Panels a) Estimate from the graph i) the break-even points e) How would your answers for break-even points and maximum profit change if i) the number of dollars of revenue per panel is increased slightly? ii) the cost function is changed to C(n)=100(2)35 ? f) What does the number that was changed in part e) ii) represent? Dollars
- Find accounting profit if total revenue is $3300 and the explicit cost is $1300A specialty bicycle manufacturer has determined the cost function for manufacturing is given by C(x) = 3x2 - 840x + 78000 where x represents the number of bicycles produced. How many bicycles should be produced to minimize the cost?A division of Chapman Corporation manufactures a pager. The weekly fixed cost for the division is $25,000, and the variable cost for producing x pagers/week in dollars is represented by the function V(x). V(x) = 0.000001r' – 0.01r? + 50x The company realizes a revenue in dollars from the sale of x pagers/week represented by the function R(x). R(x) = -0.02.r² + 150r (0 < x < 7500) (a) Find the total cost function C. C(x) = %3D (b) Find the total profit function P. P(x) = (c) What is the profit for the company if 1,600 units are produced and sold each week?
- A company makes solar panels. The company’s revenue function, in dollars, is R(n)=10n , where n is the number of panels produced. The cost function is C(n)=100(2)π/30 . R and C are shown on the graphbelow. a) Estimate from the graph i) the break-even points ii) the number of panels that should be produced for maximum profit b) Write the equation for the profit function P. c) Graph P. d) Use your graph of P to estimate the number of panels that give maximum profit. e) How would your answers for break-even points and maximum profit change if i) the number of dollars of revenue per panel is increased slightly? ii) the cost function is C(n)=100(2)π/35 changed to ? f) What does the number that was changed in part e) ii) represent?The profit of a company, in dollars, is the difference between the company's revenue and cost. The cost, C(x), and revenue, R(x), are functions for a particular company. The x represents the number of items produced and sold to distributors. C(x) = 2500 + 60x R(x) = 800x - x? a) Determine the maximum profit of the company. The maximum profit of the company is b) Determine the number of items that must be produced and sold to obtain the maximum profit. The number of items that must be produced and sold to obtain the maximum profit isCost, revenue, and profit are in dollars and x is the number of units. If the daily marginal cost for a product is MC = 4x + 100, with fixed costs amounting to $700, find the total cost function for each day. C(x) = %3D