Chapter 15, Problem 4P

(a)

To determine

To calculate: The solution of linear programming problem,

$\text{Maximize }f\left(x,y\right)=6x+8y$

Subject to the constraints,

$\begin{array}{c}5x+2y\le 40\\ 6x+6y\le 60\\ 2x+4y\le 32\\ x,y\ge 0\end{array}$

By the use of graphical method.

(b)

To determine

The solution of the linear programming problem,

$\text{Maximize }f\left(x,y\right)=1.75x+1.25y$

Subject to the constraints,

$\begin{array}{c}1.2x+2.25y\le 14\\ x+1.1y\le 8\\ 2.5x+y\le 9\\ x,y\ge 0\end{array}$

By the Simplex method.

(c)

To determine

The solution of the linear programming problem,

$\text{Maximize }f\left(x,y\right)=6x+8y$

Subject to the constraints,

$\begin{array}{c}5x+2y\le 40\\ 6x+6y\le 60\\ 2x+4y\le 32\\ x,y\ge 0\end{array}$

By the use of software.