Question

Monsanto sells genetically modified seed to farmers. It needs to decide how much seed to put into a warehouse to serve demand for the next growing season. It will make one quantity decision. It costs Monsanto $8 to make each kilogram (kg) of seed. It sells each kg for $45. If it has more seed than demanded by the local farmers, the remaining seed is sent overseas. Unfortunately, it only earns $3 per kg from the overseas market (but this is better than destroying the seed because it cannot be stored until next year). If demand exceeds its quantity, then the sales are lost—the farmers go to another supplier. As a forecast for demand, it will use a normal distribution with a mean of 300,000 and a standard deviation of 100,000.

Round your answer to 2 digits after the decimal point if it is not an integer. Do NOT use comma in your numeric answers.

Monsanto’s maximum profit for this seed is $.

The underage cost is $_______. The overage cost is $_______. The critical ratio is _______ . Monsanto should place ________ kg of seed in the warehouse before the growing season to maximize its expected profit. In such case, the expected leftover inventory will be ________ kg, the expected sales will be _______ kg, the expected profit will be $_______

Answer 1

Cost, c = 8 per kg

Domestic Sale Price, p = 45 per kg

International Sale price or Salvage Value, s = 3 per kg

Mean Demand, μ = 300,000

Standard Deviation of Demand,  σ = 100,000

A. Monsanto's maximum profit for this seed = (p-c)*μ = 37*300,000 = $11100000

B. The underage cost, Cu is = p-c = 45-8 = $37

The overage cost, Co is = c-s = 8-3 = $5

The critical ratio is = Cu / (Cu+Co) = 37/(37+5) = 0.88

z value for 0.88 from z score table = 1.18

Quantity to maximize expected profit, Q = μ+zσ = 300,000+1.18*100,000 = 418000

Monsanto should place 418000 kg of seed in the warehouse before the growing season to maximize its expected profit

In such case:

The expected lost sales = σ*L(z) = 100000*0.0584 = 5840 kg

L(z) value for z = 0.88 can be obtained from the loss function table. Here L(z) = 0.0584

The expected sales = μ-The expected lost sales = 300,000-5840 = 294160 kg

Expected leftover inventory will be = Q-The expected sales = 418000-294160 = 123840 kg

Expected Profit = (Cu*expected sales) - (Co*expected leftover inventory) = (37*294160) - (5*123840) = $10264720

The mismatch cost will be = (Cu*expected sales) + (Co*expected leftover inventory) = (37*294160) + (5*123840) = $11503120

Please like it if you have any issue mention in comment