Question

consider the R and TC functions TẾ (0) = 400 - 30 TC (Q) = 14 Q +225 • What is the optimal quantity Qt that maximizes profit!
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Answer #1

Profit = TR - TC = 440Q - 3Q^2 - 14Q - 225 = 426Q - 3Q^2 - 225

1) Differentiating profit wrt Q we get, dP/dQ = 426 - 6Q = 0

or, Q* = 71

2) Optimal profit = 426 * 71 - 3 * 71 * 71 - 225 =14898

3) the profit function must be concave which means that second order derivative at Q* must be less than 0.

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