Question
1. Find the break-even point for the firm whose cost function C and revenue function R are given. C ( x ) =150 x +30,000;
1. Find the break-even point for the firm whose cost functionCand revenue functionRare given.
C(x) =150x+30,000;R(x) =330x
(x,y) =
2. A division of a company produces income tax apps for smartphones. Each income tax app sells for$9. The monthly fixed costs incurred by the division are$30,000, and the variable cost of producing each income tax app is$4.(
a) Find the break-even point for the division.
(x,y) =
(b) What should be the level of sales in order for the division to realize a25%profit over the cost of making the income tax apps? (Round your answer up to the nearest whole number.)
______ income tax apps
3. A product may be made using Machine I or Machine II. The manufacturer estimates that the monthly fixed costs of using Machine I are $17,000, whereas the monthly fixed costs of using Machine II are $15,000. The variable costs of manufacturing 1 unit of the product using Machine I and Machine II are $12 and $19, respectively. The product sells for $50 each. (a) Find the cost functions C(x) associated with using each machine, where x is the number of units produced using that machine.
Machine I | C1(x) | = | |
Machine II | C2(x) | = |
(b) Sketch the graphs of the cost functions of part (a) and the revenue function on the same set of axes.
(c) What is the profit for each case?
500 units | $ |
600 units | $ |
700 units | $ |
4. The annual sales of Crimson Pharmacy are expected to be given by S = 2.3 + 0.4t million dollars t years from now, whereas the annual sales of Cambridge Pharmacy are expected to be given by S = 1.3 + 0.6t million dollars t years from now. When will Cambridge's annual sales first surpass Crimson's annual sales? _________ years from now
5.
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