Question

Jacava is considering producing a novelty item for golfers that will be sold through pro shops. Larry has decided on a selling price of $3.50 for the ite item's variable cost of production is $2.00 per unit, with fixed costs of $3,750. Larry has marketed his product to local pro shops and believes the demand for the item will be either 2,000 units, 3,000 units, 4,000 units, or 5,000 units. a) Set up the payoff table for Larry's decision. Determine the number of units that Larry should produce using each of the following criteria: b) (i) maximax criterion (i) maximin criterion (ii) minimax regret criterion (iv) criterion of realism (a-0.7) (v) equally likely

Answer 1

a)

Assumed all excess produced units cannot be sold further.

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

C&.uck.»)I ,.00 | 3000 |4b。 20Do 千So 12 o2So 33 so

(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:

o maximax Demand I maximo乂 units

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:

Rept Table Alternating Minim 2000 3460 566 Maxim 2000 3obo units

Under minimax regret criterion, produce 3000 units.

(iv) Criterion of realism($\alpha=0.7$​​​​​​):

In each alternative, multiply $\alpha$​ with the best return and multiply $1-\alpha$ (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 $\alpha$=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.