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