Question

A Company must decide which one of the three products to produce. For product A, the fixed costs are $100,000 with a variable cost of $3 per unit. For product B, fixed costs are $50,000 and variable costs are $6 per unit, and for product C the respective figures are $20,000 fixed and $8 variable. The marketing department projects three possible sales levels. Either the company will sell 20,000 units (probability = .7), 40,000 units (probability = .2), or 60,000 units (probability = .1). The respective per unit selling prices are for A it’d $9, for B it’s $10, and for C it’d $12.

Determine the appropriate payoff matrix and Identify any inadmissible acts.

Answer 1

The costs for the products A , B and C according to the sales levels are given below

	Number of producrs sold	Prodcut A	Product B	Product C
Sales Level - 1 with Probability 0.7	0.7 * 20000 = 14000	100000 + 14000 * 3 = 1,52,000	50000 + 14000*6 =1,34,000	20000 + 14000 *8 = 1,32,000
Sales Level - 2 with Probability 0.2	0.2*40000 = 8000	100000 + 8000 * 3 =1,24,000	50000 + 8000*6 = 98,000	20000 + 8000*8 = 84,000
Sales Level - 3 with Probability 0.1	0.1*60000 = 6000	100000 + 6000*3 = 1,18,000	50000 + 6000*6 = 86,000	20000 + 6000*8 =68,000

The revenue for the products A , B and C according to the sales levels are given below

	Number of producrs sold	Prodcut A	Product B	Product C
Sales Level - 1 with Probability 0.7	0.7 * 20000 = 14000	14000* 9 = 1,26,000	14000*10 = 1,40,000	14000*12 =1,68,000
Sales Level - 2 with Probability 0.2	0.2*40000 = 8000	8000*9 = 72,000	8000*10 = 80,000	8000*12 = 96,000
Sales Level - 3 with Probability 0.1	0.1*60000 = 6000	6000*9 = 54,000	6000*10 = 60,000	6000*12 = 72,000

The respective payput matrix is given below. (Payout = Revenue - Cost)

	Number of producrs sold	Prodcut A	Product B	Product C
Sales Level - 1 with Probability 0.7	0.7 * 20000 = 14000	-26000	6000	36000
Sales Level - 2 with Probability 0.2	0.2*40000 = 8000	-52000	-18000	12000
Sales Level - 3 with Probability 0.1	0.1*60000 = 6000	-64000	-26000	4000

The Payout is highest for Product C for Sales level 1 at a probability of 0.7

All the sales levels for Product A are returning negative payouts due to its high fixed cost

For Product B, the sales levels 2 and 3 with respective probabilities of 0.2 and 0.1 are returning negative payouts

Whereas for Product C, all the sales levels are returning positive payouts