Quantitative Analysis for Management, 13/e

Solved Problems

1. Solved Problem 7-1 Personal Mini Warehouses is planning to expand its successful Orlando business into Tampa. In doing so, the company must determine how many storage rooms of each size to build. Its objective and constraints follow:

   $$\begin{array}{lllll}\text{Maximize monthly earnings}\hfill & =\hfill & \hfill 50X_1& +\hfill & \hfill 20X_2\\ \text{subject to}\hfill & \hfill 20X_1& +\hfill & \hfill 40X_2& \le \hfill & 4,000\hfill & (\text{advertising budget available})\hfill \\ \hfill 100X_1& +\hfill & \hfill 50X_2& \le \hfill & 8,000\hfill & (\text{square footage required})\hfill \\ \hfill X_1& \le \hfill & 60\hfill & \text{(rental limit expected)}\hfill \\ \hfill X_1,X_2& \ge \hfill & 0\hfill \end{array}$$

   where

   $X_1=$ number of large spaces developed

   $X_2=$ number of small spaces developed

   Solution

   An evaluation of the five corner points of the accompanying graph indicates that corner point C produces the greatest earnings. Refer to the graph and table.

   CORNER POINT	VALUES OF X1,X2	OBJECTIVE FUNCTION VALUE ($)
   A	(0, 0)	0
   B	(60, 0) ...