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$$Simpson$,$ Inc., sells two popular brands of$$ cookies: Donna$\text{'}$s Delight and Betty$\text{'}$s Bourbon. Donna$\text{'}$s Delight goes through the Mixing and Baking$$ departments, and Betty$\text{'}$s $$Bourbon$,$ a filled$$ cookie, goes through the$$ Mixing, Filling, and Baking departments. Michael$$ Shirra, vice president for$$ sales, believes that at the current$$ price, Donna Simpson can sell all of its daily production of Donna$\text{'}$s Delight and Betty$\text{'}$s Bourbon. Both cookies are made in batches of $2$ comma $800.$

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

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

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Part $1$

Requirement $1.$ Using D to represent the batches of Donna$\text{'}$s Delight and B to represent the batches of Betty$\text{'}$s Bourbon made and sold each$$ day, formulate$$ Shirra's decision as an LP model.

Begin by determining the linear function.

Total contribution margin

$=$

$+$

Part $2$

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:

$+$

less than or equals

Part $3$

Filling$$ Department:$$

$+$

less than or equals

Part $4$

Baking$$ Department:

$+$

less than or equals

Part $5$

Requirement $2.$ Compute the optimal number of batches of each type of cookie that Donna $$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.$)$

Total

Trial

Corner $($D$,$B$)$

Contribution Margin

$1$

$(0,0)$

$2$

$(23,0)$

$3$

$(18,10)$

$4$

$(11,14)$

$5$

$(0,14)$

Part $6$

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

Corner $($D$,$B$)=$