The Gilbreth family drinks a case of Royal Cola every day, 365 days a year. Fortunately, a local distributor offers quantity discounts for large orders as shown in the table below, where the price for each category applies to every case purchased. Considering the cost of gasoline, Mr. Gilbreth estimates it costs him about $5 to go pick up an order of Royal Cola. Mr. Gilbreth also is an investor in the stock market, where he has been earning a 20 percent average annual return. He considers the return lost by buying the Royal Cola instead of stock to be the only holding cost for the Royal Cola.

T (a) Determine the optimal order quantity according to the EOQ model with quantity discounts. What is the resulting total cost per year?

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(b) With this order quantity, how many orders need to be placed per year? What is the time interval between orders?

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