Consider the following linear programming problem.Maximize P = 3x + 6y subject to the constraintsx + 3y s12-2x - 3y 2 -18x 2 0, y 2 0.(a) Write the linear programming problem as a standard maximization problem.MaximizeP=subject to< 12< 18x 2 0y 2 0(b) Write the initial simplex tableau.VPConstant1218

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Answered: Consider the following linear…

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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Maximize P = 2x + 3y + 5z subject to the constraints 2x + 3y + z 900 3x + y + zs 350 4x + 2y + 2 ≤ 400 x 20, y ≥ 0,22 0. (a) Write the linear programming problem as a standard maximization problem. Maximize P= subject to 20 y20 220 900 350 400 (b) Write the initial simplex tableau. Y Constant 900 350 400 0
State the linear programming problem in mathematical terms, identifying the objective function and the constraints. A car repair shop blends oil from two suppliers. Supplier I can supply at most 48 gal with 3.6% detergent. Supplier II can supply at most 66 gal with 3% detergent. How much can be ordered from each to get at most 100 gal of oil with maximum detergent? OA. Maximize 0.030x + 0.036y Subject to: xs48 y≤ 66 x+y≤ 100 OC. Maximize 48x + 66y Subject to: x248 y266 0.036x +0.03y2 100 OB. Maximize 0.036x+0.03y Subject to: 0≤x≤48 0sys 66 x+ys 100 D. Maximize 48x + 66y Subject to: xs48 y≤ 66 0.036x +0.03y ≤ 100
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…
Use graphical methods to solve this linear programming problem. OA. The maximum value is (Simplify your answer.) OB. There is no maximum. Maximize subject to: ... What is the maximum value of z? Select the correct choice below, and if necessary, fill in the answer box to complete your choice. z = 5x + 6y 2x-3y ≤ 12 x + y24 3x + 4y ≥ 32 x20 y20 At what point(s) does the maximum value of z occur? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The maximum value of z occurs only at the point(s) OC. There is no maximum value of z. (Type an ordered pair. Use a comma to separate answers as needed.) OB. The maximum value of z occurs at the points and at all points on the line segment connecting them. (Type an ordered pair. Use a comma to separate answers as needed.)
Use the simplex method to solve the linear programming problem. Maximize z=3x, +5x2 subject to: x, -4x2 5 55 4x, - 2x2 5 33 X, 20, x2 20. with Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Simplify your answers.) O A. The maximum is when x1 = and x2 = O B. There is no maximum.
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 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 ≥ 0
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Solve the linear programming problem by the simplex method. Maximize 40x + 30y subject to the following constraints. X + y ≤ 7 + 3y = 12 yz0 - 2x x=0, The maximum value of M is which is attained for x = and y =
Use the simplex method to solve the linear programming problem. Z = X₁ +4x₂ + x3 + 5x4 X₁ + 8x₂ + 5x₁ + x₂ + x₁20, X₂20, X3 20, x4 20 80 F3 Maximize subject to 4 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. OA. The maximum is OB. There is no maximum. View an example Get more help. 22 श्री R F % 5 t x3 + x4≤10 3x3 + x4 ≤200 G 6 when x₁ = Y H & 7 x₂ = U X3 = * 8 ▶II X4 = · ( 9 K S₁ = and $₂ =. Clear all O 0 L F10 P Check answer 4) + ||
A farmer wishes to buy some goats and cows. He has pasture for only 50 animals. Goats cost $300 each and cows $600 each. He can expect to make a profit of $250 on each goat and $350 on each cow. If he has $24000 to spend and he buys g goats and c cows, I. Formulate a linear programming model for this situation. II. Using a graph, find the numbers of goats and cows that will maximize profit. III. State the maximum profit.
Use the method of this section to solve the linear programming problem. Maximize P = x + 2y subject to 2x + 3y ≤ 12 −x + 3y = 3 x ≥ 0, y ≥ 0 The maximum is P = at (x, y) = .

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