QUESTION 6 The Sanders Garden Shop mixes two types of grass seed into a blend. Each type of grass has been rated (per pound) according to its shade tolerance, ability to stand up to traffic, and drought resistance, as shown in the table. Type A seed costs $2 and Type B seed costs $3. The blend needs to score at least 250 points for shade tolerance, 350 points for traffic resistance, and 700 points for drought resistance. Formulate linear programming model for this problem (DO NOT SOLVE for optimal solution). Shade Tolerance Traffic Resistance Type A Type B 2 2 3 2 6 Drought Resistance 3 QUESTION 7 Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade X carpet uses 40 units of synthetic fiber, requires 15 hours of production time, and needs 10 units of foam backing. Each roll of Grade Y carpet uses 30 units of synthetic fiber, requires 18 hours of production time, and needs 5 units of foam backing. The profit per roll of Grade X carpet is $150 and the profit per roll of Grade Y carpet is $110. In the coming production period, Muir has 2900 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1700 hours of production time (overtime is a possibility). The company has 1400 units of foam backing available for use. Develop a linear programming model for this problem (DO NOT SLOVE for the optimal solution). QUESTION 8 Does the following linear programming problem exhibit infeasibility, unboundedness, or alternate optimal solutions? Explain. Min 1X + 1Y s.t. 5X + 3YS 30 3X+4Y ≥ 36 Y≤7 X, Y≥O QUESTION 9 Does the following linear programming problem exhibit infeasibility, unboundedness, or alternate optimal solutions? Explain. Min 3X + 3Y s.t. 1X + 2Y ≤ 16 1X + 1Y≤ 10 5X+3Y ≤ 45 X, Y≥O QUESTION 3 Consider the following linear programming problem. Max 20x + 10Y s.t. 12X+15Y≤ 180 15X+10Y ≤ 150 3X-8Y≤0 X, Y≥O The graph below is the solution to the problem. Use this graph to answer the following question; (a) Which area (I, II, III, IV, or V) forms the feasible region? (b) Which point (A, B, C, D, or E) is optimal? (c) Which constraint are binding? (constraint involved with the optimal point) (d) Which slack variable are zero? (constraint that does not have an excess unit) A 10 E V 10 QUESTION 4 Find the complete optimal solution for the following linear programming problem (the value for X, Y, min value, S1, S2, S3) Min 5X + 6Y s.t. 3X + Y ≥ 15 X+2Y≥ 12 3X+2Y ≥ 24 X, Y≥0 QUESTION 5 For the following linear programming problem. Determine the optimal solution by the graphical solution method. Are any of the constraints redundant? If yes, then identify the constraint that is reduandant. Max X + 2Y s.t. X+Y≤3 X-2Y≥0 Y≤ 1 X, Y≥0