Problem 1: Discrete Optimization The Richardson Development Company (RDC) hasjust acquired a large plot of land in Plano. RDC has divided this land into five smaller lots, which it would now like to sell to individual buyers interested in developing them. RCD has just received a large number of bids from several potential buyers. These bids are shown in Table 1.1. Six families participated in the auction (Anderson, Baker, Chang, Dell, and Edwards) and submitted 15 distinct bids. As shown in Table 1.1., each bid species the name of the bidder, the lot(s) to buy, and the total amount to pay if the bid is accepted. Note that some bidders submitted multiple bids; for example, Edwards submitted four bids (12, 13, 14, and 15). Also, note that a bid may be for multiple lots; for example, the Anderson family wants to build a large house, so their bid 2 is for lots 2 and 3. A lot cannot be split into smaller pieces due to the town's parceling laws for residential land. Bid Amount Lot 1 Lot 2 Lot 3 Lot 4 Lot 5 Bidders Bid 1 10 1 Anderson Bid 2 25 1 1 Anderson Bid 3 23 1 _ 1 _ Baker Bid 4 20 _ 1 _ Baker Bid 5 30 1 1 Baker Bid 5 12 1 Baker Bid 1' 25 y 1 1 _ Baker Bid 8 6 _ 1 _ Chang Bid 9 5 1 Chang Bid 10 18 1 1 Chang Bid 11 11 1 Dell Bid 12 11 1 Edwards Bid 13 25 1 1 Edwards Bid 14 20 1 1 Edwards Bid 15 12 1 _ Edwards Table 1.1. Bids submitted by the potential buyers RDC would lie to generate the maximum possible revenues from the bids received. You are asked to develop a quantitative model that helps guide their decisions. Please address each of the following questions separately unless explicitly directed othenivise. Clearly identify the decisions, the objective, and the constraints in your model by (a) highlightingfcoloring cells, and (b) typing explicit comments in your spreadsheet. Your models should remain linear. If you feel that some modeling element is ambiguous and you need to make additional assumptions, please state them explicitly in your spreadsheet and proceed. 1. (25 points) Construct a discrete optimization model (i.e., with binary variables) that determines which bids should be accepted in order to maximize RDC's revenues from the auction. What is the optimal revenue that can be achieved, and which bids should be accepted? [Hint: you can assume that RDC can accept several bids from the same participant]. 2. (5 points) RDC would like to include some additional restrictions in the allocation to capture some crude fairness considerations. In addition, it also decided to allow bidders \f