Question

The weekly marginal cost functions C'(x) and the weekly marginal revenue function R'(x) of a company assembling personal computers are given by C'(x) =RM(3x^2-118x+1315) and R'(x)=RM(1000-4x), where x is the number of computers assembled per week. If the fixed costs are RM5000, find
a) the profit function
b) the increase in profit if the number of computers assembled increases from 30 to 35 per week
c) the maximum profit per week
d) the total revenue obtained and the price per unit when profit is maximised.
Please help. thank you

Answer 1

Since P(x) = R(x)-C(x)
P'(x) = R'(x)-C'(x)
max profit occurs where R'(x) = C'(x)

Since you have R' and C', you can see that

C(x) = x^3-59x^2+1315x + 5000
R(x) = 1000x-2x^2 + k
no idea what k is, since you don't specify what R is for any particular x. It is probably -5000, since there is that fixed cost, and zero production results in zero income.

Anyway, using those facts, you can answer all the questions.