1. Give the dual of each of the following linear programs:(a)maximizesubject to100x1200x2 + 300x3 + 400x4x12x2 3x3 - 4x4 ≤ 10,-5x16x27x3 + 8x4 ≥ -20,9x110x211x3 - 12x4 = 30,X1, X30,x4 ≤ 0,x2 unrestricted(b)maximizex4subject tox4x12x2 + 4x3,x42x13x2 - 5x3,x43x14x2+6x3,x1 + x2 + x3 = 1,x1, x2, x30,x4 unrestrictedHint: Remember to first rewrite all the constraints so that all variables are onthe left and the right-hand side is a constant.

We have to find the dual of the primal problem.

Answered: 1. Give the dual of each of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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13) Z-Salon profits $12 on each manicure and $18 per haircut. A manicure takes 30 minutes and a haircut takes 50 minutes. There are 5 stylists who each work 6 hours per day (that is a total of 360 min x 5 = 1800 minutes in available labor). The salon can schedule 50 appointments per day. How many manicures and how many haircuts should be scheduled each day in order order to maximize profit? What is the maximum profit? Let’s get you started. Let x = number of manicures Let y = number of haircuts OBJECTIVE The objective (goal) is to maximize profit, P. So the objective equation is P = ______________________________________________ objective equation CONSTRAINTS: 1) 2) 3) 4) Now graph the above system of inequalities (constraints) on your graph paper: Find all vertices (corner points) of your shaded region. Plug them in one at a time into the objective. Note the one which makes P the biggest. This one is our solution. Corner Pt (x,y)…
1. Give the dual of each of the following linear programs: (a) maximize 100x₁ + 200x2 + 300x3 + 400x4 subject to x1+2x2+3x3 - 4x ≤ 10, -5x16x27x3+8x4 -20, 9x1+102+11x3-12x4 = 30, X1, X30, x40, x2 unrestricted
The question is in the screenshot and the answers are listed below: A. 700 small copiers and 1,050 large copiers. B. 1,025 small copiers and 825 large copiers. C. 975 small copiers and 875 large copiers. D. 900 small copiers and 925 large copiers.
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…
1. Give the dual of each of the following linear programs: maximize 5x1 + 8x2 + x3 + 2x4 subject to (b) minimize subject to 3x1 + 3x2 + 7x3 + 8x4 ≤ 15, 2x28x3-7x4 ≥ 10, 9x16x22x3+4x4 = 5, X1, X2, X3 ≥ 0, 4 unrestricted 3x1 + 7x3 + 9x4 -x1 + 3x2x3 - 10x4≤-12, 2x1 +5x2 + 8x3 +9x4 ≥ 1, x1 +4x2+8x3 -x4, X1, X2 ≥ 0, X3 ≤ 0, 4 unrestricted Hint: Remember to first rewrite all the constraints and variables into the correct forms for minimisation!
Please can you help me with this linear programming question, I've tried seek an anser/guidance from chatgpt but it seems to get it wrong.
1. . Solve the following linear programming model graphically: minimize Z = 3x, + 6x2 pubject to 3x, + 2x2 s 18 X + x2 2 5 X S 4 x2/x, s 7/8 X1, X2 0
3. Solve the following linear programming problem. Maximize: z= 4x + 5y Subject to: x+ys4 x-y2-2 x<3 x20, y 20
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)
1. Give the dual of each of the following linear programs: (b) minimize 3x₁ +7x3 + 9x₁ subject to -₁ + 3x₂ - 3 2x1 +52 +8x3 +974 ≥ 1, 10x₁ < -12, x₁ + 4x₂ + 8x32 -4, I1, I₂ ≥ 0, X3 ≤ 0, T4 unrestricted
Identify which BFS are degenerate (if any) and which BFS are non-degenerate. Among all BFS, identify one with largest objective function value.
Maximize 3x1+2x2+4x3 subject to x1+x2+2x3 <=4 2x1+3x3 <=5 2x1+x2+3x3 <=7 x1,x2,x3 >= 0

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