Chapter 6.8, Problem 6P

Explanation of Solution

Finding the objective function:

• Contribution of Product 1 to Profit is $\text{= 15-3}\left(\text{3}\right)\text{-2 }\left(\text{2}\right)\text{-1}\left(\text{1}\right)\text{= \$1}$.
• Contribution of Product 2 to Profit $\text{= 25-4}\left(\text{3}\right)\text{-3}\left(\text{2}\right)\text{-2}\left(\text{1}\right)\text{= \$5}$
• Thus firm wishes to maximize $z=x_1+5x_2$.

Thus the LP for the problem is,

${\text{Maximize, z =x}}_{\text{1}}{\text{+5x}}_{\text{2}}$

$\begin{array}{l}{\text{3x}}_{\text{1}}{\text{+4x}}_{\text{2}}\le \text{100}\end{array}$

Explanation of Solution

b.

Payment the company should make:

• The shadow price for both skilled and unskilled labour is 0.
• Both the labour constraints are nonbinding also.
• The company is not willing to pay $\$3$ for another hour of skilled lab