Chapter 3.4, Problem 4P

Explanation of Solution

Solving LP Graphically:

Let the time spent in mine1 and mine2 be $x$ and $y$. Thus the objective function will be,

$\text{z = x + y}$

Now, let for gold and silver found be $\text{g}$ and $\text{s}$. Therefore, total earning for gold and silver will be,

$\begin{array}{l}\text{2x+1y=g}\hfill \\ \text{2x+3y=s}\hfill \end{array}$

Now we should have at least $\text{12 lb}$ of gold and at least $\text{18 lb}$ of silver to pay the monthly rent.

That is,

$\begin{array}{l}\text{g}\ge \text{12,and}\hfill \\ \text{s}\ge \text{18}\hfill \end{array}$

$\begin{array}{l}\text{2x+y}\ge \text{12 }\left(\text{1}\right)\hfill \end{array}$