Question

value: 8.00 points PA 13-3 Montanso sells genetically modified seed to farmers. It... Use Table 13.4 Montanso 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 Montanso $6 to make each kilogram (kg) of seed. It sells each kg for $43. If Montanso has more seed than demanded by the local farmers, the remaining seed is sent overseas. Unfortunately, only $2 per kg is earned 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, Montanso will use a normal distribution with a mean of 350000 and a standard deviation of 125000. If a part of the question specifies whether to use Table 13.4. or to use Excel, then credit for a correct answer will depend on using the specified method. How many kilograms should Montanso place in the warehouse before *the growing season? Use Table 13.4 and round-up rule. If Montanso put 450000 kgs in the warehouse, what is its expected b. revenue (include both domestic revenue and overseas revenue)? Use Table 13.4 and round-up rule. How many kilograms should Montanso place in the warehouse to c. minimize inventory while ensuring that the stockout probability is no greater than 10%? Use Table 13.4 and round-up rule. d. What is maximum profit for this seed?

Answer 1

Monsanto Mean demand, Standard deviation of demand, o Selling price, s Cost price, Salvage value, b 350,000 125,000 $ 43 $6 $ 2 Underage penalty, Cu Overage penalty, Co Critical ratio, F(z) Standard Normal Variate, z Optimal Quantity, =43 - 6 =6 - 2 =Cu / (Co + Cu) =Selling price - Cost price =Cost price - Salvage value = $ 37 $4 0.9024 1.3 512,500 lookup value of z in table 13.4 for F(z)>=0.9024 a) su + z*o =(450000 - 350000)/125000 lookup value of I(z) in table 13.4 for z=0.8 Specified quantity, Q Standard Normal Variate, z =(Q-w)/ (2) Expected Inventory, V =c*l(z) Expected Sales, S =Q - V Expected domestic revenue, R1 =S*s Expected overseas revenue, R2 =V*b Expected total revenue =R1+R2 450,000 0.8 0.9202 115,026 334,974 14,403,886 230,052 14,633,938 this is revenue, NOT profit. So, cost is not subtracted Target in-stock, F(z) =1 - 10% 0.90 1.3 512,500 lookup value of z in table 13.4 for F(z)>=0.9 Optimal quantity, su + zko d) Maximum profit for this seed = *Cu 12,950,000