Q#2 Solve the following linear programming problem using the graphical method and answer the following questions. Maximize Z=2x,+10x2 Subject to 10x:+4x2240 X;+6 x,224 X++2 xs14 Х, х220 I. Is any constraint binding? if so which one? II. Find the range of optimality for the coefficient in the objective function? II. Find the range of feasibility for each constraint's RHS?
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- If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.Q2. Solve the given LP problem on the right by (LP): Max Z = 2X1 + 4X2 %3D using The Graphical Solution Method. a) Find the optimal solution, determine the solution type. b) Find the optimality range for the changes in the objective coefficient c2. c) Find the feasibility range for the changes in the Right Hand Side (RHS) of one st. 3X1 + 2X2 < 12 Xị + 2X2 s 8 2X1 + X2 2 2 X1, X2 2 0 of the binding constraints.2. The following weighted normalized decision matrix Y is given. The 4 benefit criteria weights are: 0.20, 0.35, 0.40, and 0.05, respectively. Use ELECTRE method to rank the alternatives A, and A2 from best to worst. Y Alternatives A₁ A2 Criteria C3 C₁ C₂ 0.184936 0.144831 0.076150 0.318628 0.198456 0.347297 C4 0.046816 0.017556
- Formulate 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.The following payoff table shows the profit for a decision problem with two states of nature and two decision alternatives. Decision Alternative State of Nature 51 d₂ d2 (a) Use graphical sensitivity analysis to determine the range of probabilities of state of nature s, for which each of the decision alternatives has the largest expected value. d: is optimal for p(s₂) ≤ 0.2857 ; d. ✓ is optimal for p(s₂) > 0.2857 12 52 6 3 5 (b) Suppose P(s) = 0.2 and P(5₂) = 0.8. What is the best decision using the expected value approach? The best decision is d: with an expected value of 5.2 (c) Perform sensitivity analysis on the payoffs for decision alternative d₁. Assume the probabilities are as given in part (b), and find the range of payoffs under states of natures, and s₂ that will keep the solution found in part (b) optimal. As long as the payoff for s, is --?-- , then d₂ will be optimal. As long as the payoff for s₂ is --?-- Is the solution more sensitive to the payoff under state of nature…Briefly explain these terms:a. Basic variableb. Shadow pricec. Range of feasibilityd. Range of optimality
- Q1 Find the best solution for the following model using simplex MAX Z = 10X1 + 8X2 SUB TO: 4X1 + 2X2 < 80 X1 + 2X2 < 50 X1 2 0,X2 2 0A chemical company must produce exactly 1,000 kilograms of a special mixture of phosphate and potassium for a customer. The phosphate costs $5 per kilogram and potassium costs $6 per kilogram. No more than 300 kilograms of phosphate can be used, and at least 150 kilograms of potassium must be used. The problem is to determine the least-cost blend of the two ingredients. Restate the problem mathematically by: a) Showing the decision variablesb) Showing the objective functionc) Showing the constraintsd) Solve the linear programming problem by graphing. Gulf Coast Electronics is ready to award contracts to suppliers for providing reservoir capacitors for use in its electronic devices. For the past several years, Gulf Coast Electronics has relied on two suppliers for its reservoir capacitors: Able Controls and Lyshenko Industries. A new firm, Boston Components, has inquired into the possibility of providing a portion of the reservoir capacitors needed by Gulf Coast. The quality of products provided by Lyshenko Industries has been extremely high; in fact, only 0.5% of capacitors provided by Lyshenko had to be discarded because of quality problems. Able Controls has also had a high quality level historically, producing an average of only 1% unacceptable capacitors. Because Gulf Coast Electronics has had no experience with Boston Components, it estimated Boston Components' defective rate to be 11%. Gulf Coast would like to determine how many reservoir capacitors should be ordered from each firm to obtain 74000 acceptable-quality…
- Ian Langella faces a decision how large his gasoline station should be. The annual returns wil l depend on both the size of his station and number of marketing factors related to the oil in dustry and demand for gasoline. Ian develop a careful analysis based on the following table: Size of first station Market condition Market conditon Market conditon Good Fair Poor Small 50,000 20,000 -10,000 Medium 80,000 30,000 -20,000 Large 100,000 30,000 -40,000 Very large 300,000 25,000 -160,000 Develop a decision table for this decision3 II | Here are the changes to the original problem and the revised conditions for this decision-making problem: With a favorable market, John Thompson thinks a large facility would result in a net profit of $195,000 to his firm. If the market is unfavorable, the construction of a large facility would result in $185,000 net loss. A small plant would result in a net profit of $110,000 in a favorable market, but a net loss of $25,000 would occur if the market was unfavorable. Doing nothing would result in $0 profit in either market conditions. a) Create a decision table, b) What is your recommendation if you would apply the Maximax criterion (Optimistic)? Follow the guidance from your textbook and create a table. c) What is your recommendation if you would apply the Maximin Criterion (Pessimistic)? Follow the guidance from your textbook and create a table. d) What is your recommendation if you would apply the Criterion of Realism (Hurwicz Criterion) with a coefficient of realism a =…1. The marketing research department of company has recommended to the Decision-making department to launch three varieties of Chips. The Department manager has to decide one of the types of Chips to be launched under the following estimated payoffs for various levels of sales: Estimated levels of sales(in thousands) a=8 b=7 c=2 Type of Chips Potato chips 50 + a 10 + b 10 d=9 20 +c | Jack fruit chips 55 Banana chips 5 +b+c 20 + b * a 10 + 2a 1+d What will be the manager's decision under the following decision criteria's? а. Minimax Regret criterion b. Hurwicz Alpha criterion (a=0.2)