maximizesubject to- 4x1 + 1₂-₁ + x₂ ≤ 2,21-2₂ ≤ 4,x1 + x₂ ≥7,I1, I2 20 For each of the following linear programs:(1) Sketch the feasible region of the linear program and the direction of the objec-tive function.(2) Use you sketch to find an optimal solution to the program. State the optimalsolution and give the objective value for this solution. If an optimal solutiondoes not exist, state why.

Consider the given linear programming problem.maximize .Subject to:We need to draw the feasible…

Answered: For each of 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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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…
A manufacturer of refrigerators must ship at least 100 refrigerators to its two warehouses. Each warehouse holds a maximum of 100 refrigerators. Warehouse A holds 40 refrigerators already, while warehouse B has 15 on hand. It costs $10 to ship a refrigerator to warehouse A and $14 to ship one to warehouse B. How many refrigerators should be shipped to each warehouse to minimize cost? Find the objective function and the constraints for the above problem.
Just make the linear programming model of the next exercise: A company manufactures and sells two lamp models L1 and L2. For its manufacture, a manual work of 30 minutes is needed for the L1 model and 45 minutes for the L2, and a machine work of 25 minutes for L1 and 15 minutes for L2. 150 hours per month are available for manual work and 120 hours per month for the machine. Knowing that profit per unit is $150 and $100 for L1 and L2 respectively, plan production to maximize profit. Please be as clear as possible and show all the steps. Thank you very much
Write the transportation problem as a linear programming problem in terms and solvent of x and y and solve. (Indicate the number of units that should be transported from each factory to each depot and the total transportation cost.)
For this linear programming problem, formulate the linear programming model. Then, find the optimal solution graphically for the LP with only 2 variables. i.e: Max Z = 500x + 300y Subject to: 4x + 2y <= 60 (1st constraint) 2x + 4y <= 48 (2nd constraint) x, y >= 0 (non-negativity) A television producer designed a program that will include a comedy and advertisements. The advertiser insists on at least 4 minutes of advertising time. The producer insists on not more than 8 minutes of advertisement. The comedian insists on at least 5 minutes of the comedy portion. The total time allotted for the comedy and advertisement cannot exceed one hour. If it has been determined that each minute of advertising attracts 400,000 viewers and each minute of the comedy program attracts 405,000 viewers, how many minutes should be given to each of the comedy and advertisement in order to maximize the number of viewers?
The supplies, demands, and transportation costs per unit are shown on the network. (a)Develop a linear programming model for this problem; be sure to define the variables in your model. Let x11 = amount shipped from Jefferson City to Des Moines x12 = amount shipped from Jefferson City to Kansas City x13 = amount shipped from Jefferson City to St. Louis x21 = amount shipped from Omaha to Des Moines x22 = amount shipped from Omaha to Kansas City x23 = amount shipped from Omaha to St. Louis Min ???????? s.t. From Jefferson City ?????? From Omaha ??????? To Des Moines ??????? To Kansas City ???????? To St. Louis ???????????? x11, x12, x13, x21, x22, x23 ≥ 0 (b)Solve the linear program to determine the optimal solution. Amount Cost Jefferson City–Des Moines Jefferson City–Kansas City Jefferson City–St. Louis Omaha–Des Moines Omaha–Kansas City Omaha–St. Louis Total
Use the simplex method to solve the linear programming problem. Maximize: z = 2x₁ + x2 subject to: x₁ + 4x₂ ≤ 12 2x₁ + 6x₂ ≤ 4 X₁ + 2x2 ≤ 4 with x₁ ≥ 0, x₂ ≥ 0. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The maximum is when x₁ = x₂ = , S₁ = S2 = and S3 = B. There is no maximum solution to this linear programming problem.

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