PLz solve Q2 & 3 The ABC company sells another product SKU37. But this is a seas

Question

PLz solve Q2 & 3

The ABC company sells another product SKU37. But this is a seasonal product only sold in the spring. seasonal deman is drawn from normal distribution with mean 100 and Standard Deviation 25. the selling price is $40 per unit and the Purchase cost is $10 per unit. All unsold units are destroyed at no cost.

1- What is the Optimal Oreder Quantity? Solved OQ = 100 + .67 x 25 = 117

2- Suppose Frank informs you that he has heared about a new firm that for a fee of $100, will reduce the uncertainty in demand to a standard deviation of 10 unit. Should you tell Frank to hie this firm? why, why not? Please step by step

3- How much are you willing to pay to reduce the Standard deviation from 25 to 0 Zero

Explanation / Answer

(a)

Cu = cost of underage = $40 - $10 = $30
Co = cost of oerage = $10

Critical factor = Cu/(Co+Cu) = 30/(30+10) = 0.75

At optimality, the service level should be equal to the critical factor. So, Z = NORMSINV(0.75) = 0.67

So, optimal order quantity = 100 + 0.67 x 25 = 117

(b)

First, calculate the expected profit in both the cases. For the reduce std. deviation the order quantity should be Q=100 + 0.67 x 10 = 107

So, the difference in expected profit is $2870.3 - $2680.8 = $189.5. Since $100 is more than this amount, hiring this firm may be justified.

(3)

For s=0, there will be no lost sales or expected left over, So, the expected profit will be D*Cu = $3,000

So, the firm should pay $3000 - $2680.3 = $319.2

Case-I Case-II Std. Dev (s) 25 10 Q = 100+ 0.67*s 117 107 Z=NORMSINV(0.75) 0.67 0.67 Loss function, L(Z) (use tables) 0.15 0.15 Expected lost sales, L(Q) = L(Z) x s 3.7 1.5 Expected Sales, S(Q) = D - L(Q) 96.3 98.5 Expected left over, V(Q) = Q - S(Q) 20.7 8.5 Expected profit = Cu*S(Q) - Co*V(Q) 2680.8 2870.3

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