You decide you want to open a new roofing company because the closest roofing company is 100 miles away. To start, you have $750,000 to purchase the three most popular roofing tiles: Clay, Concrete, and Natural slab. The clay tiles costs you $25,000, Concrete costs $30,000, and Natural slab costs $20,000. You are able to roof 35 homes. Roofs with clay tiles can be done in one hour of time. It takes three hours for a roofer to complete a roof with concrete tiles. It takes roofer two hours to roof with natural slab tiles. On your first week, you have a small amount of roofers and can only offer 120 hours of overall labor for the first week. For each clay tile roof, you profit $6,000. You would profit $7,000 for each concrete tile roof, and $5,000 for each natural slab roof. how many of each type of roof tiles should you initially purchase in order to maximize your profit during the first week of your new roofing company?

a. Define all three decision variables

b. State the objective function [Report monetary parameters in terms of thousands of dollars. For instance, use 25 instead of 25,000 for the direct price of a clay tiles.]

c.Write the system of constraints as inequalities

d. Write the e-system using slack variables

f. Use the Simplex Method to find a combination that will produce the maximum profit and interpret.

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