financeDella Simpson, Inc., sells two popular brands of cookies: Della’s Delight and Bonny’s Bourbon. Della’s Delight goes through the Mixing and Baking departments, and Bonny’s Bourbon, a filled cookie, goes through the Mixing, Filling, and Baking departments. Michael Shirra, vice president for sales, believes that at the current price, Della Simpson can sell all of its daily production of Della’s Delight and Bonny’s Bourbon. Both cookies are made in batches of 3,000. In each department, the time required per batch and the total time available each day are as follows: Revenue and cost data for each type of cookie are as follows: 1. Using D to represent the batches of Della’s Delight and B to represent the batches of Bonny’s Bourbon made and sold each day, formulate Shirra’s decision as an LP model. 2. Compute the optimal number of batches of each type of cookie that Della Simpson, Inc., should make and sell each day to maximize operating income.
$$
\begin{matrix}
& \text{Department Minutes}\\
\text{A} & \text{B} & \text{C} & \text{D}\\
& \text{Mixing} & \text{Filling} & \text{Baking}\\
\text{Della's Delight} & \text{30} & \text{0} & \text{10}\\
\text{Total available per day} & \text{660} & \text{270} & \text{300}\\
\end{matrix}
$$
$$
\begin{matrix}
\text{A} & \text{B} & \text{C}\\
& \text{Della's Delight} & \text{Bonny's Bourbon}\\
\text{Revenue per batch} & \text{\$475} & \text{\$375}\\
\text{Variable cost per batch} & \text{175} & \text{125}\\
\text{Monthly fixed costs }\\
\text{(allocated to each product)} & \text{\$18,650} & \text{\$22,350}\\
\end{matrix}
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