(Answered)-1. Zhu Manufacturing is considering the introduction of a family - (2025 Updated Original AI-Free Solution

Question

1. Zhu Manufacturing is considering the introduction of a family of new products. Long-term demand for the product group is somewhat predictable, so the manufacturer must be concerned with the risk of choosing a process that is inappropriate. Faye Zhu is VP of operations. She can choose among batch manufacturing or custom manufacturing, or she can invest in group technology. Demand will be classified into four compartments: poor, fair, good, and excellent. The table below indicates the payoffs associated with each process/demand combination, as well as the probabilities of each possible demand level.

For example, there is a 10% (0.1) probability for the demand to be poor and 40% (0.4) of probability to have a fair demand.

Options	Demand
Poor (0.1)	Fair (0.4)	Good (0.3)	Excellent (0.2)
Batch	-$200,000	$1,000,000	$1,200,000	$1,300,000
Custom	$100,000	$300,000	$700,000	$800,000
Group Technology	-$1,000,000	-$500,000	$500,000	$2,000,000

(a) Calculate the EMVs for each of the three alternatives. For each alternative, please include at least one step of calculation and the correct answer for full credit. (12 points)

(b) What is the EVwPI in this case? Please provide the formula, at least one step of calculation and the correct answer for full credit. (6 points)

(c) What would Faye Zhu be willing to pay for a forecast that would accurately determine the demand level in the future? Hint: It is the EVPI. Please provide at least one step of calculation and the correct answer for full credit. (4 points)

2. Valu-Com Electronics manufactures two different models of telecommunication interface cards for personal computers. As summarized in the following table, each device requires different amounts of PC board, resistors, memory chips, and assembly.

	Per unit requirement
	HyperLink	FastLink
PC Board (square inches)	20	15
Resistors	28	24
Memory chips	8	8
Assembly labor (in hrs)	0.75	0.6

The wholesale price and the manufacturing cost for each model are as follows:

	Per unit revenue/cost
	HyperLink	FastLink
Wholesale Price	$189	$149
Manufacturing Cost	$136	$101

In their next production period, Valu-Com has 80,000 square inches of PC board, 100,000 resistors, 30,000 memory chips, and 5,000 hours of assembly time available. The company can sell all the products it can manufacture, but the marketing department wants to be sure that they produce at least 1,000 units of each product. Valu-Com would like to know how many of each product to produce in order to maximize the total profit.

Please formulate an LP model for this problem. (16 points)

3. Solve the following LP problem using the corner point method.

Minimize 24X + 15Y

S.T. 7X + 11Y >= 77

16X + 4Y >= 80

X, Y >= 0

Please list all corner points, calculate the corresponding objective values of each corner point, and find out the optimal solution for full credit. (14 points)

Question 1
(A) Expected Values
Batch? 0.1*(?200000)+0.4*1000000+0.3*1200000+0.2*1300000=1000000
Custom?0.1*100000+0.4*300000+0.3*700000+0.2*800000=500000
Group...