Suppose that you wish to maximize the sum X1 + X2 subject to the constraints X1≥ 0; X2 ≥ 0; X1 + X2 ≤ 3; 2X1 + X2 ≤ 4 and −2X1 + X2 ≤ 1 (a) Draw and shade the feasible region and show coordinates of corner points. (b) Find numbers X1 and X2 that maximize the sum.
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QUESTION 1
Suppose that you wish to maximize the sum X1 + X2 subject to the constraints
X1≥ 0; X2 ≥ 0; X1 + X2 ≤ 3; 2X1 + X2 ≤ 4 and −2X1 + X2 ≤ 1
(a) Draw and shade the feasible region and show coordinates of corner points.
(b) Find numbers X1 and X2 that maximize the sum.
Step by step
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- Q: Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$5 consider Cake (C) 0 -0.5 4.5 0.5 1E+30 $C$5 consider Dozen Cookies (D) 10 0 10 1E+30 1 what does the value minus .5 for the reduced cost of C mean (other than it is the change in thevalue of the coefficient in the objective function so that the solution includes a positive amountof C)?QUESTION 11 There is a company which has 2 factories at the moment and planning to build depots on 2 different locations. Each product should go from factories to depots before arriving from depots to customers. There is a fixed cost for opening a depot in location j and objective is to minimize total cost (transportation costs and fixed costs for opening depots). For this question; you need to define necessary parameters(extending transportation problem example) and develop a proper optimization model in an open form,desciribing each constraint. Convert your formulation into compact form.Given the region of feasible solutions with corner points of (0,3), (4,2), (6,3), and (6,6), find the corner point that would minimize the objective function z = x +10y and state the minimum. Question 3 options: 66 3 24 36
- Q1. General Appliance Corp. produces refrigerators at three plants: Marietta, Minneapolis and Phoenix. They ship them to major retail outlets in Chicago, Los Angeles and New York City. The accounting, production and marketing departments have provided the following information in the given tables; Plant capacities over the next planning period, retail outlet demand and unit cost of shipping between any plant and retail outlet. The company would like to minimize the cost of their transportation network by identifying how many units to ship between each plant and retail outlet. 1. Formulate this linear optimization problem by clearly listing the decision variables, objective function and constraints. 2. Create a spreadsheet model for this problem and solve it using Solver. What is the minimum cost? Plant Supply Marietta 1200 Minneapolis 800 Phoenix 1600 Retail Outlet Demand Chicago 650 Los Angeles 1450 New York City 1500…Question 2 (Linear Programming) -: The government of Ghana has available GH¢1 billion earmarked for financing the Free SHS next year. Instead of letting this money sit in a bank account for a paltry 6% risk free interest rate, it has decided to invest half of the money in four stocks on the Ghana Stock Exchange (GSE). The four stock options the government is considering and the relevant financial data are as follows: Stock A В C D Price Per Share (in GH¢) 100 50 80 40 Annual Return (in GH¢) 18 6. 8 8. Possible Loss Per Share (in GH¢) 10 6. 6. 5 However, the annual return is only a forecast (provided by experts at the ministry of finance), and could be worse or better – a risk that the government has been advised to be worry of in order not to jeopardize the finances of the Free SHS program. For example, though a share of stock A could yield a return amount of GH¢18, it is also likely it could lead to a loss of GH¢10. In order to minimize the risk (i.e. losses) associated with investing…QUESTION 2 a) b) Ferrero Candy Company makes three types of candy, which are solid, fruit and cream- filled and packages these candies in three assortments. A box of assortment I contains 4 solids, 4 fruits and 12 creams. While, a box of assortment II contains 12 solids, 4 fruits and 4 creams. Lastly, a box of assortment III contains 8 solids, 8 fruits and 8 creams. The company can manufacture up to 4800 solids, 4000 fruits and 5600 cream candies weekly. The profit each box of assortment I, II and III are RM4, RM3 and RM5 respectively. The company wishes to maximize its profit. Formulate the problem as a linear programming model. A manufacturing company produces three types of products (R, S and T). The following is an incomplete final simplex tableau for a linear programming maximization problem. X₁, X₂ and X3 represents the units of products R, S and T, respectively. S₁, S2 and S3 are the slack variables for Resources 1, 2 and 3, respectively. i. ii. A 5 4 Basic X₂ X3 X₁ Zj Cj-Zj X₁…
- Question 2 A farmer in the Blue Mountains area of Jamaica wants to decide on the crop to plant next season. He wants to plant either ganja or coffee for export to the USA but need some help. He knows that if he plants ganja and the weather in the USA is predominantly cold he earns $10,000(US per month. If the weather is warm he earns $16,000. If he plants coffee and the weather is cold he earns 13,000 and if the weather is warm he earns $14000. In 40% of the years, the weather was cold and in 60 % the weather was warm. For $600, he could buy an expert weather forecast from CWD consulting. States of Nature with Profits ($) Does not include forecast cost Decision Warm Cold weather (C) Alternatives weather(W) Ganja $16,000 $10,000 Coffee $14,000 $13000 Prior Probabilities P(W) = 0.60 P(C) = .40 Conditional probability for a given state of nature where forecasts are either Good (G) or bad (B): That is: P (G|W) = 0.80; P (B|W) = 0.20; P (G|C) = 0.10; P (B|C) = 0.90 After vou have computed…Question 2 A farmer in the Blue Mountains area of Jamaica wants to decide on the crop to plant next season. He wants to plant either ganja or coffee for export to the USA but need some help. He knows that if he plants ganja and the weather in the USA is predominantly cold he earns $10,000(US per month. If the weather is warm he earns $16,000. If he plants coffee and the weather is cold he earns 13,000 and if the weather is warm he earns $14000. In 40% of the years, the weather was cold and in 60 % the weather was warm. For $600, he could buy an expert weather forecast from CWD consulting. States of Nature with Profits ($) Does not include forecast cost Decision Warm Cold weather (C) Alternatives weather(W) Ganja $16,000 $10,000 Coffee $14,000 $13000 Prior Probabilities P(W) = 0.60 P(C) = .40 Conditional probability for a given state of nature where forecasts are either Good (G) or bad (B): That is: P (G|W) = 0.80; P (B|W) = 0.20; P (G|C) = 0.10; P (B|C) = 0.90 After vou have computed…Question 2 A farmer in the Blue Mountains area of Jamaica wants to decide on the crop to plant next season. He wants to plant either ganja or coffee for export to the USA but need some help. He knows that if he plants ganja and the weather in the USA is predominantly cold he earns $10,000(US per month. If the weather is warm he earns $16,000. If he plants coffee and the weather is cold he earns 13,000 and if the weather is warm he earns $14000. In 40% of the years, the weather was cold and in 60 % the weather was warm. For $600, he could buy an expert weather forecast from CWD consulting. States of Nature with Profits ($) Does not include forecast cost Decision Alternatives Warm weather(W) Cold weather (C) Ganja $16,000 $10,000 Coffee $14,000 $13000 Prior Probabilities P(W) = 0.60 P(C) = .40 Conditional probability for a given state of nature where forecasts are either Good (G) or bad (B): That is: P (G|W) = 0.80; P (B|W) = 0.20; P (G|C) = 0.10; P (B|C) = 0.90 After you have computed…
- Question #2 Consider the following LP formulation: Maximize Z= 2x1 + X2 -3x3+5x4 Subject to X1 +2x2 +2x3+4x4Sb1 2x1 -X2 +X3+2x4Question #3 Consider the following LP model and it is graphical solution to answer questions from a) to g). Maximize z= 4x1+5x2 Subject to: X15 .(1) 2x1+x2s12. (2) X1+2x2s12... .(3) X1, X220. .(4) 12 11 10 9 B 6 5 3 A E 1 2 3 4 6 7 10 11 12 a) What is the optimal solution x1, X2 and z? b) Determine the optimality range of the objective function coefficient c1. c) Determine the feasibility range of the right-hand side for constraint 1, 2 and 3. d) How many basic feasible solutions in this problem? e) Is there any binding constraint(s)? f) Dose any constraint has a slack? which one and by how much? g) Dose any constraint has a surplus? which one and by how much?Q-1)A glass melting furnaces feed auto plumping machines for producing the electric lamp casing (balloon),there are two main kinds can be produced, the original and the big one, they must produce at least 25 million of the original but not accede over 35 million ,and they must produce 3 million of the big one, however the ratio of the original must be at least 5 times to the big one which make a profit double the original, producing million of the big one utilize 5% Of the available materials but the original utilize 2.5% of the available materials ,For this problem ,the objective function is: Max Z =0.5X1+2X2 O MIN Z =2X1+X2 O Max Z =2X1+2X2 O Max Z =2X1+X2SEE MORE QUESTIONS