How will a change in the right-hand-side value for a constraint affect the optimalsolution?
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How will a change in the right-hand-side value for a constraint affect the optimal
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- Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.A manufacturer has the capability to produce both chairs and tables. Both products use the same materials (wood, nails and paint) and both have a setup cost ($100 for chairs, $200 for tables). The firm earns a profit of $20 per chair and $65 per table and can sell as many of each as it can produce. The daily supply of wood, nails and paint is limited. To manage the decision-making process, an analyst has formulated the following linear programming model:Max 20x1 + 65x2 – 100y1 – 200y2s.t. 5x1 + 10x2 ≤ 100 {Constraint 1}20x1 + 50x2 ≤ 250 {Constraint 2}1x1 + 1.5x2 ≤ 10 {Constraint 3}My1 ≥ x1 {Constraint 4}My2 ≥ x2 {Constraint 5}yi={1, if product j is produced0, otherwiseyi=1, if product j is produced0, otherwiseWhich of the constraints limit the amount of raw materials that can be consumed? A. Constraint 1 B. Constraint 4 C. Constraint 5 D. Constraint 1 and 4 E. Constraint 1, 2 and 3
- Combined-cycle power plants use two combustion turbines to produce electricity. Heat from the first turbine’s exhaust is captured to heat waterand produce steam sent to a second steam turbine that generates additional electricity. A 968-megawatt combined-cycle gas fired plant can be purchased for $450 million, has no salvage value, and produces a net cash flow(revenues less expenses) of $50 million per year over its expected 30-year life. Solve, a. If the hurdle rate (MARR) is 12% per year, how profitable an investment is this power plant? b. What is the simple payback period for the plant? Is this investment acceptable?Don't solve. Please give- Decision Variable Constraint Objective functionWhat combination of x and y will yield the optimum for this problem? Maximize Z = $3x + $15y Subject to: Multiple Choice x= 0, y=4 x= 0, y=3 x= 0, y=0 x= 2y=0 O x=1,y=25 2x + 4y ≤ 12 5x + 2y ≤ 10
- define your decision variables, then objective function, and constraintsFormulate decision variable, objective function, and constraints only. Eastborne Realty has $2 million available for the purchase of new rental property. After an initial screening, Eastborne reduced the investment alternatives to townhouses and apartment buildings. Each townhouse can be purchased for $282,000, and five are available. Each apartment building can be purchased for $400,000, and the developer will construct as many buildings as Eastborne wants to purchase. Eastborne’s property manager can devote up to 140 hours per month to these new properties; each townhouse is expected to require 4 hours per month, and each apartment building is expected to require 40 hours per month. The annual cash flow, after deducting mortgage payments and operating expenses, is estimated to be $10,000 per townhouse and $15,000 per apartment building. Eastborne’s owner would like to determine the number of townhouses and the number of apartment buildings to purchase to maximize annual cash flow.A car company is planning the introduction of a new electric car. There are two options for production. One is to produce the electric car at the company’s existing plant in Illinois, sharing production with its other products that are currently being produced there. If the sales of the electric car are moderate, this will work out well as there is significant capacity to produce all of the products there. However, if sales of the electric car are strong, this option would necessitate Adding a 3rd shift, which would lead to significantly higher costs. Another option is to build a new plant in Ohio. The new plant would have sufficient capacity to meet whatever level of demand for the new car. However, if sales of the new car not strong, the plant would be underutilized and less efficient. Since this is a new product, sales are hard to predict. The forecast indicates there is a 60% chance of strong sales (annual sales of 100,000), and 40% chance of moderate sales (annual sales of…
- The Rotary Club is holding a pizza sale to finance outreach projects. The Club made an agreement to purchase pizza from Pizza Hut at a 30% discount which the Rotary Club can thên resell for a profit. It is expected that of the 500 families in the community, at most 70% will buy Pizza. Based on a survey of their personal preferences, the students believe that they should order no more than 120 cheese pizzas, no more than 150 pepperoni pizzas, and no more than 100 vegetarian pizzas. They also want to make sure that at least 20% of the total pizzas are cheese and at least 50% of the pizzas are pepperoni. The standard price (before discount) for the cheese, pepperoni and vegetarian is $12, $15 and $14, respectively. The Rotary Club makes a profit of 10%, 15% and 20%, respectively, for each cheese, pepperoni, and vegetarian pizza they resell Formulate a linear programming model that would determine the optimal solution.The optimal value of one of the decision variables is zero. What should the minimum profit per bottle be for this decision variable to change to a nonzero value?Discuss the five (5) steps of the Theory of Constraints and apply each to asimulation/assumption of a constraint impacting Jaguar.