Quantitative Analysis for Management, 13/e

Solved Problem

Solved Problem M6-1

1. The following function relates the price for a product to the quantity sold:

   $$P=6-0.75Q$$

   Find the price that will maximize total revenue.

Solution

$$\begin{array}{lll}\text{Total}\text{Revenue}\hfill & =\hfill & \text{Price}\times \text{Quatity}\hfill \\ \hfill TR& =\hfill & PQ\hfill \\ \hfill TR& =\hfill & \left(6-0.75Q\right)Q=6Q-0.75Q^2\hfill \end{array}$$

So

$$TR\prime =6-0.75\left(2\right)Q$$

Setting this equal to zero and solving, we have

$$6-1.5Q=0$$

or

$$Q=4$$

Then

$$P=6-0.75Q=6-0.75\left(4\right)=6-3=3$$