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Question

For a certain company, the cost function for producing xx items is C(x)=30x+100 and the revenue function for selling xx items is R(x)=−0.5(x−70)2+2,450. The maximum capacity of the company is 130 items.

p(x)=

Profit when producing 40 items 

Profit when producing 50 items 

Answer 1

R(x) -.5(x-70)^2 +2450= -.5(x^2 -140x + 4900) + 2450=-x^2/2 +70x - 2450+2450 = -x^2/2 +70x

C(x) = 30x +100

max x = 130

p(x) = R(x)-C(x)= -x^2/2 +70x -30x -100= -x^2/2 +40x -100

p(40)= -1600/2 -+1600 -100= $700= maximum profit

p(50)=-2500/2 + 2000-100= -1350+2000= $650

max profit is when p'= 0 when -x+40=0. x=40