#3. Hartley Homes in North Texas is building a development in Northern Tarrant County and is currently negotiating with two flooring dealers on tile prices. Both dealers offer several competing tile families consisting of small {mosaic or 1 it 1], medium {4 x 4 or subway}, and large [12): 12 and 12 I: 24] tiles. Each dealer represents a different tile manufacturer, but there is reasonable overlap in styles while still permitting nuanced differences for the discriminating buyer. Both tile manufacturers deal in the high-quality ("pricey") tjle market. The dealers have offered Harey Homes competing prices for each category oftile, but the prices are only good for 90 days. To lock in these prices for the next 32 months, Hartley must sign a contract with each dealer committing to a certain minimum dollar amount for each tile category (small, medium, large]. Hartley wants to determine how many dollars to contractually guarantee each dealer to lock in these prices. Over the next 32 months, Hartley knows that they will need, at a minimum, 40,000 total SQFI' of small tile, 60,000 total SQFI' of medium tileI and 240,000 total SQFI of large tile. Additionally, Hartley knows that if they order large tile from a particular dealer, they will need to purchase at least 10% of this same square footage from the dealer's medium tile category to match designs. The prices offered per square foot are given in the table below. Prices {3501-11 Small M edium Large Dealer 1 13 8 5.5 Dealer 2 12 10 6 A. Determine a minimum cost purchasing plan for Hart ey. From that purchasing plan, determine a dollar amount for each category that Hartley can guarantee to each dealer. B. [BONUS +5 PTS] Suppose Dealer 2 offers a special incentive to encourage purchases from all three of their tile categories. Dealer 2 will discount the smallest of Hartley's three purchases by category spend [dollars for small, dollars for medium, and dollars for large] by 30%. {Note that if Hartley does not buy from all three categories, their discount is 0.} Incorporate this into your model, determine a new optimal purchase plan, and determine a dollar {spend} amount for each category that Hartley can guarantee to each dealer. Hint: You only need one new decision variable but three new constraints