Exhibit 12-2A moving company purchases large cardboard shipping boxes from a supplier. The company uses approximately 10,000 of these boxes for packing customers' belongings each year, and demand for the boxes is essentially constant throughout the year. The box supplier offers the following pricing schedule, based on the quantity of boxes ordered:The fixed cost of placing an order is $50, and the company's cost of capital is 7% per year.
$$\begin{array} { l r r r r }
\text { Unit purchase cost } & \$ 5.00 & \$ 4.50 & \$ 4.00 & \$ 3.50 \
\text { Order is more than } & 0 & 251 & 501 & 751 \
\text { Order is less than } & 250 & 500 & 750 & 1000
\end{array}$$
-Promoters of the Mulligan Golf tournament order sets of special edition clubs for $300 each that are sold during the tournament for $800 per set. Once the tournament is over, unsold sets are donated to the local Boys and Girls Clubs to be used by underprivileged youth. Based on past experience, they believe that demand for the sets will follow the Gamma distribution with alpha equal to 50 and beta equal to 20. How many sets of clubs should they order to maximize expected profit?

Question

Exhibit 12-2A moving company purchases large cardboard shipping boxes from a supplier. The company uses approximately 10,000 of these boxes for packing customers' belongings each year, and demand for the boxes is essentially constant throughout the year. The box supplier offers the following pricing schedule, based on the quantity of boxes ordered:The fixed cost of placing an order is $50, and the company's cost of capital is 7% per year.
 $$\begin{array} { l r r r r } 
\text { Unit purchase cost } & \$ 5.00 & \$ 4.50 & \$ 4.00 & \$ 3.50 \
\text { Order is more than } & 0 & 251 & 501 & 751 \
\text { Order is less than } & 250 & 500 & 750 & 1000
\end{array}$$
-Promoters of the Mulligan Golf tournament order sets of special edition clubs for $300 each that are sold during the tournament for $800 per set. Once the tournament is over, unsold sets are donated to the local Boys and Girls Clubs to be used by underprivileged youth. Based on past experience, they believe that demand for the sets will follow the Gamma distribution with alpha equal to 50 and beta equal to 20. How many sets of clubs should they order to maximize expected profit?

Quizplus · Accepted Answer

The Answer of Exhibit 12-2A moving company purchases large cardboard shipping boxes from a supplier. The company uses approximately 10,000 of these boxes for packing customers' belongings each year, and demand for the boxes is essentially constant throughout the year. The box supplier offers the following pricing schedule, based on the quantity of boxes ordered:The fixed cost of placing an order is $50, and the company's cost of capital is 7% per year.
 $$\begin{array} { l r r r r } 
\text { Unit purchase cost } & \$ 5.00 & \$ 4.50 & \$ 4.00 & \$ 3.50 \
\text { Order is more than } & 0 & 251 & 501 & 751 \
\text { Order is less than } & 250 & 500 & 750 & 1000
\end{array}$$
-Promoters of the Mulligan Golf tournament order sets of special edition clubs for $300 each that are sold during the tournament for $800 per set. Once the tournament is over, unsold sets are donated to the local Boys and Girls Clubs to be used by underprivileged youth. Based on past experience, they believe that demand for the sets will follow the Gamma distribution with alpha equal to 50 and beta equal to 20. How many sets of clubs should they order to maximize expected profit?

Exhibit 12-2A Moving Company Purchases Large Cardboard Shipping Boxes from a Supplier