Word Problem

Question

The cost to produce one laptop computer is 890.00 plus a one time fixed cost of 100,000.00 for research and development. Each laptop computer will be sold for 1520.00.

 

A. Write a formula that gives the cost C of producing x laptops

 

B. Write a formula that gives the revenue R from selling x laptop computers

 

C. Profit equally revenue minus cost. Write formula that calculates the profit P from selling X laptop computers.

 

D. Set P>0 and solve for x. Interpret your answer

Answer 1

a)

 

   C = 890 X + 100,000

 

b)

    R = 1520 X

 

c) P= 1520X - 890X - 100,000

 

d>   1520 X -890X - 100,000 >0

 

        630 X > 100,000

    

         X > 100,000/630 = 158.7

 

          Has to sell at least 159 laptop to make a profit.

         

          159 sold is a breakeven point.

Answer 2

Dear Jason,

 

(A.)  The cost, C, of producing x laptops would be 

 

C = ($890)*x + ($100,000)/x

 

(B.) Revenue, R, from selling x laptops would be

 

R = ($1520)*x

 

(C.) The profit, P, from selling x laptops is

 

P = ($1520)*x - [($890)*x + ($100,000/x)] or ($630)*x - ($100,000/x)

 

(D.) Let P = 0

 

Then

 

($630)*x - ($100,000/x) = 0

 

($630)*x = ($100,000/x)

 

Multiply both sides by x

 

($630)*x² = $100,000

 

Divide both sides by $630

 

x² = 158.73

 

x = 12.5988

 

In this case x is the minimum number of laptops that can be made and sold to start realizing a profit.  However, since no one is going to make, let alone sell, 0.5988 of a computer, the company will have to make at least 13 laptops to start realizing a profit.

 

 

 

 

Answer 3

A) C = 890x + 100,000

 

B) R = 1520x

 

C) P = 1520x - (890x + 100,000)

 

D) P = 1520x - (890x + 100,000)

 

       = 1520x - 890x - 100,000

 

     P = 630x - 100,000

 

P + 100,000 = 630x

 

x = (P + 100,000)/630

 

 

Answer 4

A. C = 100000 + 890 x

B. R = 1520 x

C. Profit = Revenue - Cost; P = R - C = 1520 x - 890 x - 100000 = 630 x - 100000

D. P > 0 => 630 x - 100000 > 0 => x > 100000/630 ≈ 158.73015873015873,

but since x has to be an integer, x > 158 for a positive profit. If x <= 158 there will be a loss.