# maximum, profits

I am looking to sell some T-shirts at my university and want to figure out the economics of the market. The total demand for these t-shirts comes from two groups: group A and group B. The demand curves for these two groups are given by the following equations:

Students; Qa = 120 − 10Pa

Faculty: Qb = 48 − 2Pb

a. I am considering buying from a vendor that would charge you $5 for every t-shirt. What would my maximum profits be if I cannot set different prices for group A and group B?

b. When buying from the same vendor who charges me $5 for every t-shirt, what are my maximum profits if I can sell t-shirts to group A and group B at different prices?

Please help me out by showing your work of how you came up with your answer.

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#### Solution Preview

a. I am considering buying from a vendor that would charge you $5 for every t-shirt. What would

my maximum profits be if I cannot set different prices for group A and group B?

The combined demand is Q = Qa + Qb= 120-10P + 48-2P = 168 - 12P

(because the price is the same for both groups)

Then we write the demand curve into:

P = (168-Q)/12 = 14 - Q/12

The total revenue is TR = P*Q = 14Q - Q^2 /12

marginal revenue is MR = dTR / dQ = ...

#### Solution Summary

Determine maximum profits.