Della 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 of sales, believes that at the current price, Della Simpsoncan sell all of its daily production of Della€™s Delight and Bonny€™s Bourbon. Both cookies aremade in batches of 3,000 cookies. The batch times (in minutes) for producing each type ofcookie and the minutes available per day are as follows:

Revenue and cost data for each type of cookie are:

REQUIRED
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 a linear programming 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.

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Department Minutes Filling Baking 10 15 300 Mixing Della's Delight Bonny's Bourbon Minutes available per day 30 15 660 15 270 Della's Delight Revenue per batch Variable cost per batch Contribution margin per batch Monthly fixed costs (allocated $ 475 S 175 300 Bonny's Bourbon $ 375 125 250 to each product) $18,650 $22,350