Calibri (Body) 11 ' Wrap Text Paste BIU a. Av Merge & Center -20 4 x fx A B D E F G H K Linear Programming (20 points) The Cycle Path shop wants to decide how many bicycles to order of each model. The 4 models it needs to order are: Bohemian (B), CitySites (C), Sea Urchin (S), and Ripcord (R). The store wants to maximize its profit from the bicycles. The unit profit, space needed, and the hours needed to assemble the bikes are shown in the table below. There are three constraints for these bicycle models that the store needs to account for (besides nonnegativity): (1) The store has 1000 feet of space for these 4 bicycle models. (2) There are 1250 hours assembly time available. (3) At least 300 bikes need to be ordered for the store's inventory. Answer the following questions in the space provided from the solved model below. (a) How many bikes of each kind should be ordered? (b) Exactly how much total space will these bikes take up? To answer (c)(d)(e), make 3 copies of this sheet, then make the appropriate changes on those sheets and rerun solver. Each question is independent of one another, e... the change in made in (c) should not apply to (d). Make sure to explicitly answer each question after you run solver. (c) If the unit profit of CitySites increases from $35 to $40, then how many bikes of each kind should be ordered? What is the maximum profit then? (d) Suppose the available assembly time increases from 1250 hours to 1350 hours. What is the new maximum profit? (e) Suppose because of customer demand, the following two constraints must be added: B+R >=100 C+S >= 100 where B - units of Bohemian to order, C = units of CitySites to order, etc. Add these new constraints and solve. Now how many bikes of each kind should be ordered? K M 19 20 21 22 23 B D E F G H (e) Suppose because of customer demand, the following two constraints must be added: BR>100 C+S > 100 where B - units of Bohemian to order, C- units of CitySites to order, etc. Add these new constraints and solve. Now how many bikes of each kind should be ordered? 24 25 26 City Sites B Bohemian 4 6 45 S Sea Urchin 3 4 R Ripcord 3 4 27 Answers a) Bohemian City Sites Sea Urchin Ripcord 4 5 35 30 Total space b) c) Bohemian CitySites Sea Urchin Ripcord Max Profit 27 28 29 Data 30 31 Space (ft) 32 Assy time (hours) 33 Unit profit (S) 34 35 36 37 38 Model 39 40 41 Solution 42 43 Profit 44 Space 45 Assy Time 46 Min. Inventory 47 d) I New max profit Bohemian City Sites Sea Urchin Ripcord e) CitySites LHS Bohemian 25 Sea Urchin 275 Ripcord 0 RHS Slack 0 45 4 6 35 4 5 1 30 3 4 27 3 4 9375 925