Question

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Answer 1

a. Underage cost C_u = Selling price - cost = $27 - $11 = $16

here Salvage value is $-5 as Goop Needs to spend to scrap unused materials

So, Overage cost C_o = Cost - Salvage value = $11 - ($-5) = $16

F(Q) = C_u/(C_u+C_o) = 16/(16+16) = 16/32 = 0.5

From distribution function table we can see Z = 0 for F(Q) = 0.5

Let, Q_max = Gallon to be purchased to maximize profit

Q_max = μ + z σ = 300+0*150 = 300 (Ans)

b. z = (Q - μ )/ σ

or,z = (175-300)/150 = -125/150 = -5/6 = -0.83

In-stock probability = From distribution function table we get, Φ ( - 0.83) = 0.2033

Out-of-stock probability = 1-0.2033 =0.7967  (Ans)

c) z = (Q - μ )/ σ

or, z = (350-300)/150 = 0.33

From distribution function table L(0.33) =  0.2555

Average Lost Sales = σ *L(0.33) = 150*0.2555 = 38.325

Expected Sales = Mean sales - Lost sales = 300 - 38.325 = 261.675 = 261.68 (Rounding to 2 decimal places) (Ans)

d) z = (Q - μ )/ σ

or, z = (450-300)/150 = 1

From distribution function table L(1) =  0.0833

Average Lost Sales = σ *L(1) = 150*0.0833 = 12.495

Average Sales = Mean Demand – Average Lost Sales = 300 – 12.495 = 287.505.

Average Left Over Inventory = Q – Average Sales = 450-287.505 =162.495

Average cost of disposal = Disposal cost per gallon * Average Left Over Inventory = $5*162.495 =$812.475 = $812.48 (Rounding to 2 decimal places)(Ans)