A. In 1 year, a health food manufacturer produces and sells 240,000 cases of vit

Question

A. In 1 year, a health food manufacturer produces and sells 240,000 cases of vitamins. It costs $2 to store 1 case for 1 year and $15 set up to run a batch. How many batches should be produced annually in order to minimize the cost? B. Your uncle runs a small vitamin booth in the mall. he has some storage space but not a lot so he has to order wisely. If he needs 25 cases for the year, pays $35 per case in addition to the $30 processing fee each time he orders, and estimates that it costs him $7 per case to store it in his booth- how many cases should he order at a time? C. Your uncle just called- boy is he mad. The manufacturer just called and said the price per case of vitamins is going up $4. He just got in a big shipment and is worried that with the increase in price his customers will not buy the product. Does the elasticity of demand indicate this may occur? If there is reason to believe that the demand will change, what percent of change should your uncle expect? (Note: recent marketing studies indicate that the demand for this vitamin is q=400-0.2p^2)

Explanation / Answer

Ans A – We can find the answer by the EOQ approach.

EOQ = SQRT (2 x Quantity x Set up cost / Storage cost) = SQRT (2 x 240000 x 15 / 2) = 1897

Number of batches = 240000 / 1897 = 127

Ans B – EOQ = SQRT (2 x quantity x order cost / storage cost) = SQRT (2 x 25 x 30 / 7) = 15

He should order 15 cases at a time.

Ans C – Elasticity of demand does not indicate that the demand will fall drastically with the price increase. With a $4 increase in price will change the quantity by 0.2 x 4 ^2 = 0.64

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