Written out on paper please 1. 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.(a)(b)maximizesubject tomaximizesubject to- 4x₁ + x₂₁ + x₂ ≤ 2,x1 - 2x₂ ≤ 4,x₁ + x₂ ≥ 7,x1, x2 > 0₁ + 2x₂-₁ + 2x₂ ≤ 4,1+ 3x2 ≤ 12,x1, x₂ > 0

Answered: Image /qna-images/answer/c6e20ecd-42d3-4a3a-a724-fa61fbd28415.jpg

Answered: 1. For each of the following linear…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section: Chapter Questions

Problem 10CT: Sketch the region corresponding to the system of constraints. Then find the minimum and maximum...

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A company manufactures two fertilizers, x and y. Each 50-pound bag of fertilizer requires three ingredients, which are available in the limited quantities shown in the table. The profit on each bag of fertilizer x is 6 and on each bag of y is 5. How many bags of each product should be produced to maximize the profit? Ingredient Number of Pounds in Fertilizer x Number of Pounds in Fertilizer y Total number of Pounds Available Nitrogen 6 10 20,000 Phosphorus 8 6 16,400 Potash 6 4 12,000
In Example 3, if the accountant earns a profit of 100 on each individual return and a profit of 175 on each business return, find the maximum profit. An accountant prepares tax returns for individuals and for small businesses. On average, each individual return requires 3 hours of her time and 1 hour of computer time. Each business return requires 4 hours of her time and 2 hours of computer time. Because of other business considerations, her time is limited to 240 hours, and the computer time is limited to 100 hours. If she earns a profit of 80 on each individual return and a profit of 150 on each business return, how many returns of each type should she prepare to maximize her profit?
Redo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of Kenyan beans, and 150 grams of French roast beans and the gourmet blend contains 100 grams of Colombian beans, 350 grams of Kenyan beans, and 50 grams of French roast beans. This time the merchant has on hand 30 kilograms of Colombian beans, 15 kilograms of Kenyan beans, and 15 kilograms of French roast beans. Suppose one bag of the house blend produces a profit of $0.50, one bag of the special blend produces a profit of $1.50, and one bag of the gourmet blend produces a profit of $2.00. How many bags of each type should the merchant prepare if he wants to use up all of the beans and maximize his profit? What is the maximum profit?
1b and 2b written out on paper please
1a and 2a please written out
A company produces two types of solar panels, A and B, that sell for $4 million and $3 million per thousand units, respectively. The cost of producing x thousand of type A and y thousand of type B is x - 2xy + 8y + 8x - 85y -6. Find the values of x and y that maximize the company's profits. [Note: (revenue) - (cost).] Profit = The company will achieve a maximum profit by selling solar panels of type A and selling solar panels of type B.
A bakery makes 600 specialty breads—multigrain or herb—each week. Standing orders from restaurants are for 100 multigrain breads and 200 herb breads. The profit on each multigrain bread is $8 and on herb bread, $10. How many breads of each type should the bakery make to maximize profit? How, if at all, do the maximum profit and optimal production policy change if the bakery has no standing orders?
Valencia Products make 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 first 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. When the linear optimization model below was solved, it was found that the maximum profit was obtained by producing 0 LaserStop models and 454.55 SpeedBuster models for a profit of $61,818.80. Complete parts a through c. Maximize Profit 125 L+136 S 17 L+ 11 S≤5000 6L+8S≤4500 L20 and S20 a. Modify the data in the model to create a problem with alternative optimal solutions. Choose the correct model below. OA Maximize Profit=136 L+136 S 11 L+11 Ss 5000 8 L+8 S≤4500 L20 and 520 (Component A) (Component B) C. Maximize Profit=125 L+136 S 17 L+11 S 25000 6L+8 S24500 L20 and $20 OB. Maximize Profit 125 L…
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 optimal solution and give the objective value for this solution. If an optimal solution does not exist, state why. (a) (b) maximize subject to maximize subject to - 4x1 + x₂ x₁ + x₂ ≤ 2, x1 - 2x₂ ≤ 4, x₁ + x₂ ≥ 7, X1, X20 ₁ + 2x₂ x₁ + 2x₂ ≤ 4, x1 + 3x2 ≤ 12, X1, X2 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 optimal solution and give the objective value for this solution. If an optimal solution does not exist, state why.
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…
Valencia Products make 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 and find an optimal solution, ensuring that the number of units produced is integer-valued. How much difference is there between the optimal integer solution objective function and the linear optimization solution objective function? Would rounding the continuous solution have provided the optimal integer solution? Maximize Profit = 124 L + 134 S 18 L + 11 S≤ 3000 6 L+8 S≤ 2500 L≥0 and S≥0 (Component A) (Component B) (Nonnegativity) The optimal integer solution is to produce (Round to the nearest whole number as needed.) LaserStop and SpeedBuster. This solution…

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