Chapter 5, Problem 11RP

a.

Explanation of Solution

Cost function

• Let ${\text{c}}_{\text{i}}$ be the number of cars produced at plant $\text{i}$.
• From the LINDO output, the cost function value is determined by the equation $\text{C}\left(\text{x}\right)\text{ = FC + V}\left(\text{x}\right)$

b.

Explanation of Solution

Smallest decrease

• 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 r

c.

Explanation of Solution

Production target

• From the LINDO output, the total cost increases by 70.
• Hence the cost of producing more cars is 70...

d.

Explanation of Solution

Fall of firm’s cost

• From the LINDO output, when each type of labour is payed for an extra hour then its objective function coefficient will be increased to 45.
• Here the productivity of labour is decreased from 1.5 hours to 1 hour per automobile.
• Hence as a result, the solution remains optimal...

e.

Explanation of Solution

Increase in cost

• From the LINDO output, if 2000 autos are produced, then the allowable increase will be 600.
• As a result, here the current solution remains optimal...

f.

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:

  $\text{ Key row value = Current key row va}$