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A monopolist supplies a market wit the inverse demand function P = 100 - (X +...

A monopolist supplies a market wit the inverse demand function P = 100 - (X + Y)
where X is output in plant 1 and Y output in plant 2. The total cost functions are Cx=X²  
Cy = 1.25Y² . Each plant has a fixed maximum capacity of 12 units of output.

a) Suppose the firm is able to expand capacity by one unit at only one plant which plant should it choose?

b) Suppose now that the firm is able to invest in expanding capacity by four units in total. How should that be allocated between the two plants?

c) If instead the firm is able to invest 10 units of capacity output, how should that be allocated?

Illustrate and explain answer in each case.

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