Chapter 2.7, Problem 6CFU

To determine

To find: the minimum value of printing cost, and if not possible to find then state whether this situation is infeasible, has alternate optimal solutions, or is unbounded.

Answer to Problem 6CFU

$10

Explanation of Solution

Given information:

Cost of printing brochure = 8¢ =$0.08

Cost of printing flier = 4¢ =$0.084

Pages required for brochure = 3

Pages required for flier = 2

Maximum pages = 600

Minimum Brochure need = 50

Minimum flier need = 150

Calculation:

Let the brochure and flier be x and y respectively. The inequalities and the function for minimizing cost derived from the data are as follows:

  $\begin{array}{l}x\ge 50\\ y\ge 150\\ f\left(x,y\right)=0.08x+0.4y\end{array}$

The graph for the given inequalities is as follows:

  

The vertices of the polygon boundary are $\left(50,150\right),\left(50,225\right)$ and $\left(100,150\right)$ . Put these points in the $f\left(x,y\right)$ and check the minimum value as follows:

  $\begin{array}{c}f\left(50,50\right)=0.08\left(50\right)+0.4\left(50\right)\\ =\$10\\ f\left(50,225\right)=0.08\left(50\right)+0.4\left(225\right)\\ =\$13\\ f\left(100,150\right)=0.08\left(100\right)+0.4\left(150\right)\\ =\$14\end{array}$

Thus, the minimum cost is $10.