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Linear Optimization Model for Oakton Manufacturing to Maximize Profit

1. Oakton Manufacturing makes two types of rocking chairs known as the Big and Small models. Each chair requires four legs and two rockers but differing numbers of wooden dowels. Each Big chair requires four short dowels and eight long dowels while each Small chair requires eight short dowels and four long dowels. Each Big chair contributes \$10 in profit while each Small chair contributes \$12. The company has 900 legs, 400 rockers, 1,200 short dowels, and 1,056 long dowels available. The company wants to maximize its profit while also ensuring that it makes at least half as many Big chairs as Small chairs.

(a) Build a table that shows the capacity usage breakdown and profit contribution of the two products. the capacity usage breakdown and profit contribution of the two products

Legs Rocks Short Dowels Long Dowels Profit Per Unit (USD)

Big Chair 4 2 4 8 10

Small Chair 4 2 8 4 12

Total90040012001056

Note: The table on slide 4 of the "8.2" slide may give you an idea about how to display the capacity usage of the two products. That example happens to use fractions but you will use whole numbers here. You will need to add the profit contributions to that. If you do this in Excel, please paste your table into your Word document. No interpretation is needed here.

(b) Formulate a linear optimization model for this problem. (Such as the model on slide 16 of the "8.2" slides – that slide is not numbered, but it’s the one after slide 15.)

Hint: The first line should be "Max:" with an equation. The next line is "Subject to:" with several constraints.

(c) Build a spreadsheet representation of the model, and then solve it using Solver. (Such as the examples shown in “9.1”-“9.3” slides.) Identify the production amounts of each product and total profit at the solution point. In other words, report how many  of each type of chair they should produce and how much profit that will generate. Keep the Solver solution as part of your spreadsheet. (i.e., save your file after solving the problem.)