Using the mean and standard deviation Willmar Company produces a variety of food products. Its 16 oz. bottles of concentrated black cherry juice cost $8.00 to produce and sell for $12 each. Sales are 10,000 bottles per month.

The company has received a number of letters from its customers, complaining that its 16 oz. bottles of black cherry concentrate contain less than 16 ounces of product. The bottles are filled by automatic equipment that can be set to fill any amount, but the amount actually placed into containers varies with a standard deviation of .5 ounce. The quantities dispensed by the equip- ment are normally distributed. Currently, the equipment is set to dispense 16 ounces of product. Because of the complaints, management decides that it must set the equipment to minimize the probability of under filling the bottles. The manager of quality control wants the equipment adjusted so that there is a 98 percent probability that the bottles will contain at least 16 ounces of product. The marketing manager believes that 95 percent is a high enough probability.

REQUIRED

a. Determine how to set the equipment in order to have a 98 percent probability of filling bottles with at least 16 ounces of product.

b. Calculate the additional cost of the product caused by adjusting the equipment as required in partfl.

c. Determine how to set the equipment in order to have a 95 percent probability of filling bottles with at least 16 ounces of product.

d. Calculate the additional cost of the product caused by adjusting the equipment as required in part c.

e. What is the difference in monthly production cost between the marketing manager's and the quality control manager's proposals?