A&C Distributors is a company that represents many outdoor products companies and schedules deliveries to discount stores, garden centers, and hardware stores. Currently, scheduling needs to be done for two lawn sprinklers, the Water Wave and Spring Shower models. Requirements for shipment to a warehouse for a national chain of garden centers are shown below. $\begin{array} { c | c | c | c | c | c } \text { Month } & \begin{array} { c } \text { Shipping } \\\text { Capacity }\end{array} & \text { Product } & \begin{array} { c } \text { Minimum } \\\text { Requirement }\end{array} & \begin{array} { c } \text { Unit Cost } \\\text { to Ship }\end{array} & \begin{array} { c } \text { Per Unit } \\\text { Inventory Cost }\end{array} \\\hline \text { March } & 8000 & \text { Water Wave } & 3000 & .30 & .06 \\& & \begin{array} { c } \text { Spring } \\\text { Shower }\end{array} & 1800 & .25 & .05 \\\hline \text { April } & 7000 & \begin{array} { c } \text { Water Wave } \\\text { Spring } \\\text { Shower }\end{array} & \begin{array} { c } 4000\\\\4000\\\end{array} & \begin{array} { c } .40\\\\.30\\\end{array} &\begin{array} { c } .09\\\\.06\\\end{array} \\\hline \text { May } & 6000 & \text { Water Wave } & 5000 & .50 & .12 \\& & \text { Spring shower } & 2000 & .35 & .07\end{array}$ Let S_ij be the number of units of sprinkler i shipped in month j, where i = 1 or 2, and j = 1, 2, or 3. Let W_ij be the number of sprinklers that are at the warehouse at the end of a month, in excess of the minimum requirement.
a.Write the portion of the objective function that minimizes shipping costs.
b.An inventory cost is assessed against this ending inventory.Give the portion of the objective function that represents inventory cost.
c.There will be three constraints that guarantee, for each month, that the total number of sprinklers shipped will not exceed the shipping capacity.Write these three constraints.
d.There are six constraints that work with inventory and the number of units shipped, making sure that enough sprinklers are shipped to meet the minimum requirements.Write these six constraints.

Question

A&C Distributors is a company that represents many outdoor products companies and schedules deliveries to discount stores, garden centers, and hardware stores. Currently, scheduling needs to be done for two lawn sprinklers, the Water Wave and Spring Shower models. Requirements for shipment to a warehouse for a national chain of garden centers are shown below.

\begin{array} { c | c | c | c | c | c } \text { Month } & \begin{array} { c } \text { Shipping } \\\text { Capacity }\end{array} & \text { Product } & \begin{array} { c } \text { Minimum } \\\text { Requirement }\end{array} & \begin{array} { c } \text { Unit Cost } \\\text { to Ship }\end{array} & \begin{array} { c } \text { Per Unit } \\\text { Inventory Cost }\end{array} \\\hline \text { March } & 8000 & \text { Water Wave } & 3000 & .30 & .06 \\& & \begin{array} { c } \text { Spring } \\\text { Shower }\end{array} & 1800 & .25 & .05 \\\hline \text { April } & 7000 & \begin{array} { c } \text { Water Wave } \\\text { Spring } \\\text { Shower }\end{array} & \begin{array} { c } 4000\\\\4000\\\end{array} & \begin{array} { c } .40\\\\.30\\\end{array} &\begin{array} { c } .09\\\\.06\\\end{array} \\\hline \text { May } & 6000 & \text { Water Wave } & 5000 & .50 & .12 \\& & \text { Spring shower } & 2000 & .35 & .07\end{array}

Let S_ij be the number of units of sprinkler i shipped in month j, where i = 1 or 2, and j = 1, 2, or 3. Let W_ij be the number of sprinklers that are at the warehouse at the end of a month, in excess of the minimum requirement.
a.Write the portion of the objective function that minimizes shipping costs.
b.An inventory cost is assessed against this ending inventory.Give the portion of the objective function that represents inventory cost.
c.There will be three constraints that guarantee, for each month, that the total number of sprinklers shipped will not exceed the shipping capacity.Write these three constraints.
d.There are six constraints that work with inventory and the number of units shipped, making sure that enough sprinklers are shipped to meet the minimum requirements.Write these six constraints.

Quizplus · Accepted Answer

The Answer of A&C Distributors is a company that represents many outdoor products companies and schedules deliveries to discount stores, garden centers, and hardware stores. Currently, scheduling needs to be done for two lawn sprinklers, the Water Wave and Spring Shower models. Requirements for shipment to a warehouse for a national chain of garden centers are shown below. $$\begin{array} { c | c | c | c | c | c } \text { Month } & \begin{array} { c } \text { Shipping } \ \text { Capacity } \end{array} & \text { Product } & \begin{array} { c } \text { Minimum } \ \text { Requirement } \end{array} & \begin{array} { c } \text { Unit Cost } \ \text { to Ship } \end{array} & \begin{array} { c } \text { Per Unit } \ \text { Inventory Cost } \end{array} \ \hline \text { March } & 8000 & \text { Water Wave } & 3000 & .30 & .06 \ & & \begin{array} { c } \text { Spring } \ \text { Shower } \end{array} & 1800 & .25 & .05 \ \hline \text { April } & 7000 & \begin{array} { c } \text { Water Wave } \ \text { Spring } \ \text { Shower } \end{array} & \begin{array} { c } 4000\\4000\ \end{array} & \begin{array} { c } .40\\.30\ \end{array} &\begin{array} { c } .09\\.06\ \end{array} \ \hline \text { May } & 6000 & \text { Water Wave } & 5000 & .50 & .12 \ & & \text { Spring shower } & 2000 & .35 & .07 \end{array}$$ Let S_ij be the number of units of sprinkler i shipped in month j, where i = 1 or 2, and j = 1, 2, or 3. Let W_ij be the number of sprinklers that are at the warehouse at the end of a month, in excess of the minimum requirement. a.Write the portion of the objective function that minimizes shipping costs. b.An inventory cost is assessed against this ending inventory.Give the portion of the objective function that represents inventory cost. c.There will be three constraints that guarantee, for each month, that the total number of sprinklers shipped will not exceed the shipping capacity.Write these three constraints. d.There are six constraints that work with inventory and the number of units shipped, making sure that enough sprinklers are shipped to meet the minimum requirements.Write these six constraints.

A&C Distributors Is a Company That Represents Many Outdoor Products