Chapter 5, Problem 12RP

a.

Explanation of Solution

Optimal solution

• The new optimum solution value or profit is calculated by the given formula:

  $\text{New value = Old value – }\left(\text{Key column value × Key row value}\right)\text{ / Key value}$

• The key row value can be calculated by the given formula:

  $\text{ Key row value = Current key row value / Ke}$

b.

Explanation of Solution

Optimal solution

• The new optimum solution value or profit is calculated by the given formula:

  $\text{New value = Old value – }\left(\text{Key column value × Key row value}\right)\text{ / Key value}$

• The key row value can be calculated by the given formula:

  $\text{ Key row value = Current key row value / Key element value}$

• Here ${\text{p}}_{\text{i}}$ is the unit of product $\text{i}$ produced, $\text{SL}$ is the hour of skilled labour purchased and $\text{UL}$ is the hour of unskilled labour purchased

c.

Explanation of Solution

Pay for extra hour of time

• From the output, the dual price of machine 1 is row 2 which is 10.52.
• Dual price of machine 2 is row 3 which is 6...

d.

Explanation of Solution

Pay for an extra hour

• From the LINDO output, the dual price of skilled labour which is row 4 is 0...

e.

Explanation of Solution

Monthly profit

• Here skilled labour is in excess supply already.
• As a result, there is a slack of 16.67 hours left of skilled labour.
• Hence additional skilled labour would...