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.