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Word Problem

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
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4 Answers

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.
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.
 
 
 
 

Comments

The R&D cost is incurred no matter how many computers are made.
Sorry, Jason, I was trying to do things in such a way as to break up that R&D cost on a "per unit" basis and obviously got it wrong.  Chaitali and Parviz got it right.
100,000 is going to be distributed among the entire numbers of laptop sold, therefore:
 
   C = 630 X + 100,000  ( is a total costs of producing X numbers of laptop)
 
      
 
   
Your equation for
 
  C = $890X + 100,000
 
     $890 X = cost of production of X unit
       Total cost , should be calculated by adding fixed cost + variable cost ($890X)
       However you have added per unit cost of fixed cost 100,000/x.
        100, 000 is fixed and is not depended on number of production.
         You see that in next question asks how many unit needed to be produced to incur profit.

Comment

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.
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