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Q2B)By applying an appropriate method of optimisation, locate the quantity of components the firm should produce and the maximum profit it can earn per month

Profit maximisation occurs at SMC=MR



TVC = aQ + bQ2 + cQ3

AVC = a + bQ + cQ2

SMC = a + 2bQ + 3cQ2

Weekly TVC= 46Q – 0.0085 Q2 + 0.00001 Q3

Weekly AVC= 46 – 0.0085 Q + 0.00001 Q2

Weekly SMC = 46 – 2(0.0085 )Q + 3(0.00001) Q2


Weekly demand (P) = A+BQ

=245 – 0.2Q

Marginal revenue (MR) =A+2BQ


= 245+0.4Q


46-0.017Q+0.00003Q2= 245+0.4Q

Solve: 0.00003Q2-0.383Q-199=0for Q*

To fnd that , use Q*= -b + √ b^2 – 4ac _____________ 2a

Q=-(+0.383) + √ (-0.383)^2 – 4(: 0.00003)(199) _____________ 2(0.00003)

Q = - 0.383 + √ 0.766 -0.02388 _____________ 0.00006

Q = - 0.383 + √ 0.7422 _____________ 0.00006
Q =-0.383 +0.8615 0.00006


Or Q =-0.383-0.8615 0.00006


Q=7975.1716 or Q=-20,741.6666


Q* =-20,741.6666( not applicable as quantity cannot be negative

(Let’s assume there are 4 weeks in a month)

So from the calculation , we use 7975X4=31,900 for our amount of quantity per month figures

The company should produce at quantity 31,900 in order to maximize profit per month

Maximum profit it can earn per month

Let’s assume there are 4 weeks in a month

P=245 – 0.2(7975)




Let’s assume…...

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