Question

29.

A firm has to decide which one of three new products to launch. The profitability of each product depends on the level of demand. The research conducted by the firm suggests that the demand for these types of products can be high, medium, and low with different probabilities. The decision problem faced by the firm is presented in the form of a payoff matrix (profits) as shown below:

	States of Nature
		High	Medium	Low
Decision Alternatives		s1	s2	s3
Product A	d1	$100,000	$65,000	$0
Product B	d2	$80,000	$50,000	$25,000
Product C	d3	$75,000	$50,000	$20,00

Suppose the probability of demand level being high is 0.35, medium 0.45 and low 0.2. What is the maximum expected value and the optimal decision?

	$64,250 & launch product B
		$64,250 & launch product C
		$64,250 & launch product A
		$52,750 & launch product A
		$55,500 & launch product A

Answer 1

Ans:

		High	Medium	Low
Decision Alternatives		s1	s2	s3	Expected value
Product A	d1	$100,000	$65,000	$0	$64,250.00
Product B	d2	$80,000	$50,000	$25,000	$55,500.00
Product C	d3	$75,000	$50,000	$20,000	$52,750.00

Expected value for d1=100000*0.35+65000*0.45+0*0.2=64250

Expected value for d2=80000*0.35+50000*0.45+25000*0.2=55500

Expected value for d3=75000*0.35+50000*0.45+20000*0.2=52750

Correct option is $64,250 & launch product A