Given the details below, how many X2 should be produced to reach the maximum profit? Maximize: 3X1 + 2 X2 Subject to: 2X1 + X2 ≤ 100 X1 + X2 ≤ 80 X1 ≤40 X1, X220
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- Maximize p = 7x + 6y + 3z subject to x + y + z ≤ 150 x + y + z ≥ 100 x ≥ 0, y ≥ 0, z ≥ 0. p= (x, y, z)=Imagine that there are 100 similar yet independent houses (located in different geographic areas), each facing the same six possible outcomes next year with equal probability: no loss; small loss; medium loss; large loss; huge loss; catastrophic loss. Explain why it’s easier to insure all 100 houses than to insure just one. What difference does it make if these 100 similar houses are no longer independent (e.g. they are located in the same neighborhood)?For a certain civil engineering system, it is sought to maximize the benefits, which is given by the expression: Z=3x+5y. The decision variables are x (the amount of resource type 1 to be used) and y (the amount of resource type 2 to be used). • The amount of resource type 1 should be at least 3 units. • The amount of resource type 2 should be at least 3 units. The difference between the amount of ● resource type 2 and the amount resource type 1 should not exceed 6. • The total amount of resource types 1 and 2 should not exceed 12 units. a. Identify the obiective function for this problem. b. Identify and write the constraints. c. Provide a sketch graph for the constraint set. d. Clearly show the feasible region. e. Label all extreme points (or vertices) of the feasible region and indicate their coordinates. f. Solve the optimization problem.
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- A firm that plans to expand its product line must decide whether to build a small or a large facilityto produce the new products. If it builds a small facility and demand is low, the net present valueafter deducting for building costs will be $400,000. If demand is high, the firm can either maintainthe small facility or expand it. Expansion would have a net present value of $450,000, and maintaining the small facility would have a net present value of $50,000.If a large facility is built and demand is high, the estimated net present value is $800,000. If demandturns out to be low, the net present value will be – $10,000.The probability that demand will be high is estimated to be .60, and the probability of low demandis estimated to be .40.a. Analyze using a tree diagram.A firm that plans to expand its product line must decide whether to build a small or a large facilityto produce the new products. If it builds a small facility and demand is low, the net present valueafter deducting for building costs will be $400,000. If demand is high, the firm can either maintainthe small facility or expand it. Expansion would have a net present value of $450,000, and maintaining the small facility would have a net present value of $50,000.If a large facility is built and demand is high, the estimated net present value is $800,000. If demandturns out to be low, the net present value will be – $10,000.The probability that demand will be high is estimated to be .60, and the probability of low demandis estimated to be .40. 1- Compute the EVPI 2- Determine the range over which each alternative would be best in terms of the value of P ( low demand )Chemitronix Ltd. is a microchips manufacturing company. It was found that the business is at the maturity stage, demanding some change. After rigorous research, management came up with the following decision variables Expansion: 45% chance of gaining 1,500,000; 55% chance of losing X New Product: 50% chance of gaining 900,000; 50% chance of losing 545959 What must have been the value of expansion loss if expansion and new product will result to the same expected monetary values?
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