ythos.content.blackboardcdn.com/5c1c67a3c99fc/2929686?X-Blackboard-Expiration=D1606219200000&X1/ 1QUESTION 1Swearingen and McDonald, a small furniture manufacturer, produces fine hardwood tables andchairs. Each product must go through three stages of the manufacturing process: assembly,finishing, and inspection. Each table requires 12 hours of assembly, 20 hours of finishing, and 2hours of inspection. Each chair requires 4 hours of assembly, 16 hours of finishing, and 3 hoursof inspection. The profit per table is $150 while the profit per chair is $100. Currently, each weekthere are 300 hours of assembly time available, 220 hours of finishing time, and 30 hours ofinspection time. To keep a balance, the number of chairs produced should be at least twice thenumber of tables. Also, the number of chairs cannot exceed 6 times the number of tables. (Youmay use QM-software for this problem. All the detailed output should be displayed).a) Formulate this as a linear programming problem. Carefully define all decision variables.b) Show the graph of the feasible region indicating all the relevant corner pointsc) Find the optimal solution to this LP and find the maximum profits.QUESTION 2A community farm has 6000 square kilometers of land available to plant wheat and millet. Eachkilometer square of wheat requires 9 gallons of fertilizer and insecticide and 4 hour of labor toharvest. Each square kilometer of millet requires 3 gallons of fertilizer and insecticide and 1 hourof labor to harvest. The community has at most 40,500 gallons of fertility and insecticide and atmost 5250 hours of labor for harvesting. If the profits per square kilometer are $60 for wheat and$40 for millet, how many square kilometers of each crop should the community plant in order tomaximize profits? What is the maximum profit? Hint: x is the number of square kilometers ofwheat and y is the number of square kilometers of millet.(A complete solution is required for this problem - No software)a

Please note that you have posted multiple questions in one post, so one question is answered as per the guidelines. (a) Decision variables: T= Number of tables to be produced C = Number of chairs to be produced Profit from one table is $150 and the profit from one chair is $100 Total profit: 150T+100C Objective function: Max Z = 150T+100C The constraints to produce the products are as follows. 1. Assembly related: 12T+4C≤300 2. Finishing related: 20T+16C≤220 3. Inspection related: 2T+3C≤30 4. Production related (Number of chairs should be at least twice the number of tables) C=2TC-2T=0 5. Production related (number of chairs should not exceed 6 times the number of tables) C≤6TC-6T≤0 In order to insert the graph, use the following steps. Add the data in QM software as follows. Click on solve and select graph in solution. Optimal solution: We used integer as the number of chairs and the number of tables cannot be in decimal form. Number of chairs to be produced = 6 Number of tables to be produced = 3 Total profit = (150*3)+(100*6)=450+600=$1050