Elimination/substitution equations

Question

The function C(x) = 1.19x + 7.5 represents the cost of producing x stainless steel widgets. R(x) = 1.69x represents the revenue from selling x of them. Find the following.

a. Number that must be sold to break even

b. Profit from selling 500

c. Profit or loss from selling 200 at regular price and 300 at half price.

Answer 1

For 200 widgets the cost is c(x)=1.19*200+7.5=245.5.

To break even r(245.5)/1.69=145.27 is to be sold.

c(500)=602.50 (Use formula)

r(x)= /1.69=356.51 To be sold/even.

By selling 143.49 more; you'll bring in an extra r(x)=$242.50.

Since you're cutting a price in half the 300 is now 150.

Cost of 350 is c(x)=424.00

r(350)=591.5

-424=$167.5 profit

500 see above. you're

Answer 2

a. Break even is when cost = revenue. So set them equal and solve for x.

b. Profit = Revenue - Cost. Plus in x = 500 in the revenue and cost equations then compute the profit.

c. At half price the revenue is (1/2)R(x). Cost is the same.

Profit = R(200) + (1/2)R(300) - Cost(500)