## Answers

**a)**

Assumed all excess produced units cannot be sold further.

Below are the images with the calculations and the payoff table:

**(b)**

(i) Maximax criterion:

Select maximum pay-off in each alternative and then, choose the maximum of such maximum of pay-offs which is shown below:

Under Maximax criterion, produce 5000 units.

(ii) Maximin criterion:

Select the minimum pay-off in each alternative and then, choose the maximum of such minimum pay-offs as shown here under:

Under maximin criterion, produce 2000 units.

(iii) Minimax regret criterion:

First, draw the regret table where, regret =best pay-off - pay-off received. Select maximum regret in each alternative and then, choose the minimum of such maximum regrets which is the following:

Under minimax regret criterion, produce 3000 units.

(iv) Criterion of realism():

In each alternative, multiply with the best return and multiply (i.e., 1-0.7 =0.3) with the worst return and add them. Then, the highest of such sums is to be chosen.

2000 units:

0.7(-750)+0.3(-750) = -750

3000 units:

0.7(750)+0.3(-2750) = -300

4000 units:

0.7(2250)+0.3(-4750) = 150

5000 units:

0.7(3750)+0.3(-6750) =600

The highest of above four sums is $600 in case of 5000 units. Thus, the best alternative under criterion of realism with =0.7 is to produce 5000 units.

(v) Equally likely:

In each alternative, find the average of pay-offs and then choose the highest of such averages as shown in the below image:

The highest average of -125 is at 3000 units. So, the best decision under equally likely criterion is to produce 3000 units.