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HW1-solution

# HW1-solution - 1 BB 1.3 a b c The production manager wants...

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1. BB 1.3 a) The production manager wants to minimize total costs TC = P E *E + P L *L . b) The constraint is to produce Q = 200 units, so the manager must choose E and L so that EL = 200. c) The endogenous variables are E and L , because those are the variables over which the production manager has control. By contrast, the exogenous variables are Q , P E , and P L because the production manager has no control over their values and must take them as given. d) , min . . 200 E L E L P E P L s t EL + = e) The Langrange is ( 200) E L P E P L EL λ + + . FOC wrt. E: 1 0 2 E L P E λ + = ; FOC wrt. L: 1 0 2 L E P L λ + = . From the above two equations, we get E L P L P E = or 2 E L = . Then by the constraint EL = 200 we have L=100 2 and E=200 2 . . 2. BB 1.13 a) The objective function is the number of new SUVs sold, which we can denote by Q ( F, G ). b) The constraint is that total spending must be less than or equal to \$2million, or TS \$2 million.

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