Consider the following linear program and answer the following questions. Max 3A + 48 s.t. -1A+28≤9 1A+28 13 24+ 18 ≤16 A, B z 0 (a) Write the problem in standard form. Max 3A + 46+0 s.t. -14 + 28 + $₁ 1A+28 2A +18 ],)s;+ 0 ₂⁰ x A, B, S₁, S₂, S., V (b) Solve the problem using the graphical solution procedure. (A. B)= S₂ - 0 5₂ 0 S₂ x x (c) What are the values of the three slack variables at the optimal solution? ])₁₂ + ( [0 $3 ],)s, - 13 -16
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- Problem 7-19 eBook Given the linear program Max 3A +48 s.t. Y -1A+ 1A + 2A + s.t. 28 ≤ 8 2B ≤ 12 18 ≤ 16 Α, Β 2 0 a. Write the problem in standard form. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Al+ A+ A+C A+ B+ B B+ B B b. Select the correct graph that shows the optimal solution for the problem. S1 S1 + + S₂ + S2 + S3 53 A, B, S1, S2, S3 A Q☆Briefly explain these terms:a. Basic variableb. Shadow pricec. Range of feasibilityd. Range of optimalityMaximize C- 16A + 21B subject to 9A +15B $22 10A + 3B ≤ 29 and A≥0, B20. What is the optimal value of A? O 2.444 O 0.000 39.11 O 4.222
- Maximize Profit=123 L + 136 S 17 L+11 S≤ 3000 6 L+9 S≤2500 L20 and S20 (Availability of component A) (Availability of component B) Show Transcribed Text Implement the linear optimization model and find an optimal solution. Interpret the optimal solution. The optimal solution is to produce LaserStop models and SpeedBuster models. This solution gives the possible profit, which is $. (Type integers or decimals rounded to two decimal places as needed.)STAR Co. provides paper to smaller companies whose volumes are not large enough to warran paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The cutting patterns have been established: 1 2 Pattern 12ft. 15ft. 30ft. Trim Loss 0 4 1 10 ft. 3 0 7 ft. 8 0 0 4 ft. 2 1 2 1 ft. 5 2 3 1 1 ft. Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 2(12)+1(15) + 2(30) = 99 hand for the coming week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. hand will be sold on the open market at the selling price. No inventory is held. Number of: 3Please show how to solve b
- LPP Model Maximize P = 12x + 10y Subject to : 4x + 3y < 480 2x + 3y < 360 X, y 2 0 Which of the following points (x, y) is feasible? A) ( 120, 10) B ( 30, 100 ) c) ( 60, 90 ) D) ( 10, 120 )Q1. Build a linear programming model to develop an investment portfolio that minimizes total risk under the above constraints. a) Define the decision making variables. b) Show the objective function. c) Show the constraints. Q2. What is the optimal solution and what is the value of the objective function? Show the relevant portion of the Solver’s output. Fully interpret the results. Q3. What are the objective coefficient ranges for the four stocks? Show the relevant portion of the Solver’s output. Fully interpret these ranges. Q4. Suppose the investor decides that the annual rate of return no longer has to be at least 9% and agrees to at minimum level of 8%. What does the shadow price associated with this constraint indicate about a possible change in total risk that could occur from this lower rate of return? Show the relevant portion of the Solver’s output. Fully interpret the results.Problem 3: Let L(x, y) be the statement “x loves y”, where the domain for both x and y consists of all people in the world. Use quantifiers to express each of the following statements.1. Everybody loves Jerry.2. Everybody loves somebody.3. There is somebody whom everybody loves.4. Nobody loves everybody.5. There is somebody whom Lydia does not love.6. There is somebody whom no one loves.7. There is exactly one person whom everybody loves.8. There are exactly two people whom Lynn loves.9. Everybody loves himself or herself.10. There is someone who loves no one besides himself or herself.
- Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? A. Product_2 B. Product_1 C. Product_3 Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 13 5 $B$3 Product_2 175 0 25 8 9 $B$4 Product_3 0 −1.5 25 11 3 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700Aa6. please solve with formulas not excellFopic 4- Linear Programming: Appli eBook Problem 9-05 (Algorithmic) Kilgore's Deli is a small delicatessen located near a major university. Kilgore's does a large walk-in carry-out lunch business. The deli offers two luncheon chili specials, Wimpy and Dial 911. At the beginning of the day, Kilgore needs to decide how much of each special to make (he always sells out of whatever he makes). The profit on one serving of Wimpy is $0.46, on one serving of Dial 911, $0.59. Each serving of Wimpy requires 0.26 pound of beef, 0.26 cup of onions, and 6 ounces of Kilgore's special sauce. Each serving of Dial 911 requires 0.26 pound of beef, 0.41 cup of onions, 3 ounces of Kilgore's special sauce, and 6 ounces of hot sauce. Today, Kilgore has 21 pounds of beef, 16 cups of onions, 89 ounces of Kilgore's special sauce, and 61 ounces of hot sauce on hand. a. Develop a linear programming model that will tell Kilgore how many servings of Wimpy and Dial 911 to make in order to maximize his profit today.…