Dixie Simpson, Inc., sells two popular brands of cookies: Dixie's Delight and Beth's Bourbon. Dixie's Delight goes through the Mixing and Baking departments, and Beth'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, Dixie Simpson can sell all of its daily production of Dixie's Delight

and Beth's Bourbon. Both cookies are made in batches of $3,300.$

$($Click the icon to view the time required per batch and the total time available.$)$

$($Click the icon to view the revenue and cost data.$)$

Read the requirements.

Requirement $1.$ Using $D$ to represent the batches of Dixie's Delight and $B$ to represent the batches of Beth's Bourbon made and sold each day, formulate Shirra's decision as an LP model.

Begin by determining the linear function.

Total contribution margin $=$

Next specify the constraints for each department. $($If an input field is not used in the table, leave the input field empty; do not select a constraint.$)$

Mixing Department:

Filling Department:

$+$

$$

$+$

Baking Department:

$+$

$$

$+$ Requirement $2.$ Compute the optimal number of batches of each type of cookie that Dixie Simpson, Inc., should make and sell each day to maximize operating income.

Calculate the total contribution margin for each corner point, then we can select the optimal number of batches. $($For trials with a $$0$ balance, make sure to enter $"0"$ in the appropriate field.$)$

Select the corner point that represents the optimal number of batches of each type of cookie, to maximize operating income.

Corner$(D,B)=$Data table

In each department, the time required per batch and the total time

available each day are as follows: