Math 1010 Assignment 4 [20 ] 1. Use the corner point me

Math 1010 Assignment 4 [20 ] 1. Use the corner point method to solve the following linear programming problems. (a) Find the maximum value of 75Zxy=+ subject to the following constraints: 74532721231800xyxyxyxy+=+=-=-== (b) Find the minimum value of 43Zxy=+ subject to the following constraints: 1522315412000xyxyxyxy+=+=+=== [10] 2. Use the corner point method to solve the following linear programming problem. Find the maximum value of M = 3x + 4y subject to the following constraints. 002169525.xyxyxyxy==+=+=+= [10 ] 3. The Better Boat Company manufactures two types of water craft: canoes and kayaks. The manufacturing of each canoe requires 8 hours in the carpentry shop and 3 hours in the finishing shop. The manufacturing of each kayak requires 5 hours in the carpentry shop and 4 hours in the finishing shop. Each month the company has available 800 hours in the carpentry shop and 470 hours in the finishing shop. The profit on the sale of each canoe is $100 and the profit on the sale of each kayak is $120. Determine the number of canoes and the number of kayaks to manufacture each month so as to maximize the profit. [10 ] 4. Use the simplex method to maximize p = 5x + 4y + 3z subject to the constraints: 00030236032484xyzxyzxyzxyz===++=++=++= [10 ] 5. Use the simplex algorithm to find the maximum value of p = 8x + 8y + 12z subject to the constraints: x + y + z 40 2x + y + 3z 90 3x + 2y + 4z 84 x0 y0 z0. ===== 1
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