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2. D.G.H.M. Inc. makes two different grades of cement mix for driveway paving for their clients. Many of the jobs they do are seasonal, but some are unaffected by weather. The mixes, referred to as Rough, and Smooth are made by combining different percentages of the same three ingredients as listed below. Rough has a popularity for things like land fill and basements walls, whereas Smooth is significantly more popular for floors, garages and walkways. Mix\Ingredients limestone silica sand Silk Selling Price (per pound) Rough 80% 10% 10% $3.55 Smooth 25% 30% 45% $5.60 The ingredients (Limestone and Silica Sand) are purchased from a vendor in another province to avoid marketing competition and as such they have to be shipped in. The final shipping costs per load are indicated in the following table Ingredients Pounds per shipment Cost per Shipment Pounds available Limestone 250 $650 1000 Silica Sand 400 $300 2400 Silk 100 $400 3000 In a recent marketing survey, D.G.H.M. Inc. has determined that over the next year they want to manufacture between 1000 and 2250 pounds of Rough cement; and at least 1500 pounds of Smooth cement. They also want to make sure that the amount of Smooth cement is never less than that of double the amount of Rough cement. If X is the number of pounds of Rough coment manufactured and Y is the number of pounds of Smooth cement manufactured, what combination of X and Y (integer only solutionis) would maximize the company profits. For this problem clearly derive the Linear program Graph this problem and clearly indiente tliefensible options Clearly determine the solution to the problem using the method of points (be smart about which points you have to evaluate based on the graph of the objective function Create a excel prend sbect, use solver to solve it and discuss/interpret the dual values and range of optimality for all constraints and coefficients. What does these range of optimnilities tell us? Discuss the results of this question from a business perspective involving the constraints given