Problema Solution
The cost to produce one laptop computer is $890 plus a one time fixed cost of $100,000 for research and development. Each laptop computer will be sold for $1520.
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 and solve for x. Interpret your answer.
Answer provided by our tutors
(a)
The cost of producing the first laptop is
890*1 + 100,000 = $100,890
The cost of producing two laptops is
890*2 + 100,000 = $101,780
And, in general, the cost of producing x laptops is
890*x + 100,000
Thus
C = 890x + 100,000
(b)
Because the company receives $1520 for each laptop, the revenue for x laptops is given by
R = 1520x
(c)
Profit equals revenue minus cost, so
P = R - C = 1520x - 890x - 100,000 = 630x - 100,000
(d) 630x - 100,000 > 0
x > 100000/630
x > 158.73
the company must sell at least 159 laptops to yield a positive profit.