5. Maximize Z = 3x + 4y and the constraints are : x- y <-1; -x +y <0 and x, y 2 0.
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Can you Solve the given linear programming problems by simplex method:
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- An investor has $621,000 to invest in bonds. Bond A yields an average of 8% and the bond B yields 7%. The investor requires that at least 5 times as much money be invested in bond A as in bond B. You must invest in these bonds to maximize his return. This can be set up as a linear programming problem. Introduce the decision variables: x= dollars invested in bond Ay= dollars invested in bond B Compute x+y. $ . Round to the nearest cent. Investor Matt has $152,000 to invest in bonds. Bond A yields an average of 9.2% and the bond B yields 8.4%. Matt requires that at least 4 times as much money be invested in bond A as in bond B. You must invest in these bonds to maximize his return. What is the maximum return? $ per year. Round to the nearest cent. Investor Dan has $607,000 to invest in bonds. Bond A yields an average of 8.5% and the bond B yields 8.4%. Dan requires that at least 4 times as much money be invested in bond A as in…Solve the following linear programming problem. You are taking two dietary supplements daily: Supplement A and Supplement B. An ounce of supplement A contains 9 units of calcium, 8 units of vitamin D, and 5 units of sodium. An ounce of supplement B contains 2 units of calcium, 4 units of vitamin D, and 3 units of sodium. Your goal is to get at least 90 units of calcium and at least 120 units of vitamin D from the supplements daily, while at the same time reducing the amount of sodium that you will get. How many ounces of each supplement should you take daily to reach your goals? Ounces of Supplement A = Blank 1. Fill in the blank, read surrounding text. Ounces of Supplement B = Blank 2. Fill in the blank, read surrounding text. How many units of sodium will you get daily under these circumstances? Units of Sodium = Blank 3. Fill in the blank, read surrounding text.I am learning about this for the first time and I did this question but feel like I did not answer the parts correctly. Please could I see how an expert would answer the whole problem to compare. the question is to construct an LP model where all the variables constrained are positive.
- Zmax = 3x1 + 7x2 %3D Subject to 2x1 + 3x2< 6 X1 + X2 < 4 X1 2 0, X2 2 0 In the starting simplex tableau, the basic variables are slack variables. The objective value in the next simplex table isFormulate but do not solve the following exercise as a linear programming problem.A division of the Winston Furniture Company manufactures x dining tables and y chairs. Each table requires 40 board feet of wood and 2 labor-hours. Each chair requires 16 board feet of wood and 4 labor-hours. In a certain week, the company has 2800 board feet of wood available and 560 labor-hours.If the profit for each table is $50 and the profit for each chair is $18, how many tables and chairs should Winston manufacture to maximize its profits P in dollars? Maximize P = subject to the constraints board feet labor-hours x ≥ 0 y ≥ 0this is a linear programming problem. one image is the required information and the other image is the question.
- Use Excel to solve the linear programming problem.At one of its factories, a manufacturer of televisions makes one or more of four models of HD units (without cases): a 20-in. LCD, a 42-in. LCD, a 42-in. plasma, and a 50-in. plasma. The assembly and testing time requirements for each model are shown in the table, together with the maximum amounts of time available per week for assembly and testing. In addition to these constraints, the supplier of cases indicated that it would supply no more than 290 cases per week and that of these, no more than 40 could be for the 20-in. LCD model.Use the profit for each television shown in the table to find the number of completed models of each type that should be produced to obtain the maximum profit for the week. Find the maximum profit. 20-in. LCD sets 42-in. LCD sets 42-in. plasma sets 50-in. plasma sets profit $ 20-in.LCD 42-in.LCD 42-in.Plasma 50-in.Plasma TotalAvailable Assembly time…Formulate but do not solve the following exercise as a linear programming problem.A division of the Winston Furniture Company manufactures x dining tables and y chairs. Each table requires 40 board feet of wood and 2 labor-hours. Each chair requires 16 board feet of wood and 5 labor-hours. In a certain week, the company has 2800 board feet of wood available and 500 labor-hours.If the profit for each table is $50 and the profit for each chair is $18, how many tables and chairs should Winston manufacture to maximize its profits P in dollars? Maximize P = subject to the constraints board feet labor-hours x ≥ 0 y ≥ 0Below is the Simplex table of a basic feasible solution (BFS) of a linear programming problem where some values are represented by letters. RHS X5 f X2 X3 X4 a 3 b 4 1 e h -5 -3 -1 -1 1 2 d 1 -4
- Formulate a linear programming problem that can be used to solve the following question. An individual needs a daily supplement of at least 380 units of vitamin C and 64 units of vitamin E and agrees to obtain this supplement by eating two foods, I and II. Each ounce of food I contains 34 units of vitamin C and 4 units of vitamin E, while each ounce of food II contains 20 units of vitamin C and also 12 units of vitamin E. The total supplement of these two foods must be at most 29 ounces. Unfortunately, food I contains 22 units of cholesterol per ounce and food II contains 32 units of cholesterol per ounce. Find the appropriate amounts of the two food supplements so that cholesterol is minimized. X = ---Select--- y = --Select--- ---Select--- | F = Subject to (objective function) (total ounces of food) (units of vitamin C) (units of vitamin E) x ---Select--- 0, y ---Select--- 0 (nonnegativity constraint)Formulate a linear programming problem that can be used to solve the following question. A firm has plants in Boston and Baltimore that manufacture three models of hot tubs: regular, fancy, and super. In one day the Boston plant can manufacture 44 of the regular model, 32 of the fancy model, and 20 of the super model, and costs $4500 per day to operate, whereas the Baltimore plant can manufacture 12 of the regular model, 16 of the fancy model, and 58 of the super model, and costs $2000 per day to operate. At least 300 of the regular model, 320 of the fancy model, and 680 of the super model are needed. How many days must each plant operate in order to minimize the cost? ---1pəjəs-- = X y = ---Select--- ---Select--- v F = (objective function) Subject to (regular models) (fancy models) (super models) 0A---1pajas--Formulate a linear programming problem that can be used to solve the following question. A dealer has 8900 pounds of peanuts, 6000 pounds of almonds, and 3800 pounds of cashews to be used to make two mixtures. The first mixture wholesales for $2.40 per pound and consists of 60% peanuts, 30% almonds, and 10% cashews. The second mixture wholesales for $3.20 per pound and consists of 15% peanuts, 45% almonds, and 40% cashews. How many pounds of each mixture should the dealer make to maximize revenue? x = ---Select--- y = ---Select--- ---Select--- v|F= Subject to (objective function) (pounds of peanuts) (pounds of almonds) (pounds of cashews) x ---Select--- 0, y ---Select--- 0 (nonnegativity constraint)
