A product's demand curve can be expressed as Q = 20 - P and total cost is TC = 10Q + Q² . The firm's profit-maximization problem is:

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The firm's profit-maximization problem is to choose the optimal quantity Q that maximizes profit π. π = TR - TC where TR is total revenue and TC is total cost. TR can be obtained by multiplying the demand function Q = 20 - P by price P: TR = P(20 - P) = 20P - P^2 TC is given as TC = 10Q + Q², which can be simplified as TC = 10Q + 10P^2 Substituting TR and TC in the profit equation: π = 20P - P^2 - 10Q - 10P^2 π = 20P - 11P^2 - 10(20 - P) - 10P^2 π = -21P^2 + 220P - 200 The optimal quantity Q that maximizes profit can be found by differentiating the profit equation with respect to Q and setting it equal to zero: dπ/dQ = -21Q + 220 = 0 Q = 10.476 Substituting this value of Q back into the demand function gives us the optimal price P that maximizes profit: P = 20 - Q = 9.524 Therefore, the best choice is B, 11eb11da_1ca6_85f1_ad38_a10d8c3dd42d_TB3883_11, which gives the optimal profit-maximizing quantity and price of Q = 10.476 and P = 9.524 respectively.

A Product's Demand Curve Can Be Expressed as Q =