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. maximizesubject to₁ +2%2-₁ + 2x₂ ≤ 4,1+ 3x2 ≤ 12,I1, I2 20

Given linear programming problem isMaximize .Subject to:We have to find an optical solution of the…

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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Formulate the following problem as a linear programming problem (DO NOT SOLVE): A dietician can purchase an ounce of chicken for $0.25 and an ounce of potatoes for $0.02. Each ounce of chicken contains 13 units of protein and 24 units of carbohydrates. Each once of potatoes contains 5 units of protein and 35 units of carbohydrates. The minimum daily requirements for the patients under the dieticians' care are 45 unites of protein and 50 units of carbohydrates. How many ounces of each type of food should the dietician purchase for each patient so as to minimize costs and at the same time insure the minimum daily requirements of protein and carbohydrates? (Let x1 equal the number of ounces of chicken and x2 the number of ounce of potatoes pruchased per patient)
Use the simplex method to solve the linear programming problem. Maximize: z = 2x₁ + x₂ subject to: X₁ + 3x₂ ≤ 12 2x₁ + 3x₂ ≤ 6 X₁ + X₂ ≤ 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 =₁ $₂ = | and = " $3 B. There is no maximum solution to this linear programming problem.
I am not sure how to solve this. A ball manufacturer produces soccer balls, footballs, and volleyballs. The manager feels that restricting the types of balls produced could increase revenue. The following table gives the price of each ball, the raw materials cost, and the profit on each ball. The monthly profit must be at least $10,000, and the raw materials costs must be no more than $20,900. How many of each type of ball should be produced to maximize the revenue, and what is the maximum revenue?
Use the simplex method to solve the linear programming problem. Maximize subject to: O B. There is no maximum. with $₂ =10x₁ +10x₂ 4x1 + 2x2 $22 5x1 + x2 ≤20 2xy + 2x₂ ≤30 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The maximum is when x₁ = x₂ =, $₁ = | (Type integers or simplified fractions.) = Z= X₁ 20, x₂ 20 and $3 =
A company produces two types of solar panels, A and B, that sell for $5 million and $4 million per thousand units, respectively. The cost of producing x thousand of type A and y thousand of type B is x - 3xy + 6y + 16x - 65y - 5. Find the values of x and y that maximize the company's profits. [Note: Profit = (revenue) – (cost).] The company will achieve a maximum profit by selling solar panels of type A and selling solar panels of type B.
Use Excel. Write the linear program, optimal solution and objective function value on the worksheet. A small backpack manufacturer carries four different models of backpacks, made of canvas, plastic, nylon, and leather. The bookstore, which will sell the backpacks exclusively, expects to be able to sell between 15 and 40 of each model. the store has agreed to pay $35.50 for each canvas backpack, $39.50 for each plastic backpack, $42.50 for each nylon backpack, and $69.50 for each leather backpack that can be delivered by the end of the week. One worker can work on either canvas or plastic, can complete a backpack in 1.5 hours, and will charge $7.25 per hour to do the work. This worker can work a maximum of 90 hours durin the week. another worker can sew backpacks made of nylon fabric. He can complete a bag in 1.7 hours, will charge $8.25 per hour to work, and can work 42.5 hours in the next week. A third worker has the ability to sew leather. He can complete a backpack in 1.9…
The area of a triangle with sides of length a, b, and c is s(s - a)(s – b)(s - c), where s is half the perimeter of the triangle. We have 60 feet of fence and want to fence a triangular-shaped area. Part A: Formulate the problem as a constrained nonlinear program that will enable us to maximize the area of the fenced area, with constraints. Clearly indicate the variables, objective function, and constraints. Hint: The length of a side of a triangle must be less than or equal to the sum of the lengths of the other two sides. Part B: Solve the Program (provide exact values for all variables and the optimal objective function).
please solve using excel thank you
please can you help with the following question with alternative working out thanks a lot
Use the simplex method to solve the linear programming problem. Maximize: z = 2x1 + x2 subject to: x1 + 3x2 ≤ 12 2x1 +5x2 ≤ 6 X1 x1 + 2x2 ≤ 4 with x₁ ≥0, X2 ≥0. R Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The maximum is ☐ when X₁ = when x₁ = x2 = 0, s₁ = 0, $2 = 0, and S3 = ☐ X1 OB. There is no maximum solution to this linear programming problem.
For the linear program Max 2A + 3B 1A+2B < 6 5A+3B 15 A, B ≥ 0 find the optimal solution using the graphical solution procedure. What is the value of the objective function at the optimal solution?
Valencia Products makes automobile radar detectors and assembles two models: LaserStop and SpeedBuster. Both models use the same electronic components. After reviewing the components required and the profit for each model, the firm found the following linear optimization model for profit, where L is the number of LaserStop models produced and S is the number of SpeedBuster models produced. Implement the linear optimization model on a spreadsheet and use Solver to find an optimal solution. Interpret the optimal solution, identify the binding constraints, and verify the values of the slack variables. Maximize Profit = 124 L +137 S 17 L+12 S≤5000 5L+9S≤4500 L≥0 and S≥O (Availability of component A) (Availability of component B) Implement the linear optimization model and find an optimal solution. Interpret the optimal solution. The optimal solution is to produce 0 LaserStop models and SpeedBuster models. This solution gives the maximum possible profit, which is $. (Type integers or…

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