Martin Oritz, purchasing manager for the True Taco fast food chain, was contacted by a sales person for a food service company. The sales person pointed out the high breakage rate that was common in the shipment of most taco shells. Martin was aware of this fact, and noted that the chain usually experienced a 10% to 15% breakage rate. The sales person then explained that his company recently had designed a new shipping container that reduced the breakage rate to less than 5%, and he produced the results of an independent test to support his claim. When Martin asked about price, the sales person said his company charged $25 for a case of 500 taco shells, $1.25 more than True Taco currently was paying. But the sales person claimed that the lower breakage rate more than compensated for the higher cost, offering a lower cost per usable taco shell than the current supplier. Martin, however, felt that he should try the new product on a limited basis and develop his own evidence. He decided to order a dozen cases and compare the breakage rate in these 12 cases with the next shipment of 18 cases from the current supplier. For each case received, Marin carefully counted the number of usable shells. The results are shown in the table below.

New Supplier	Current Supplier
468	444
474	449
474	443
479	440
482	439
478	448
469	441
484	434
470	427
463	446
468	452
	442
	450
	444
	433
	441
	436
	429

Questions: 

a. Use @Risk and draw the cumulative probability distribution for both the new and current supplier data. Find the Median (50th percentile), the 5th and the 95th percentile values. 

b. The objective is to find the lowest expected cost per usable taco shell. Create a decision tree to compute the expected value for the two suppliers. Use the EP-T approximation (pages 328-330) where the probability of the median is assigned 63% and the 5th and 95th percentile probabilities are assigned 18.5% each. In the model setting, under the calculation tab, use payoff formula and the formula is the cost divided by the number of usable taco shells.