Consider the following linear programming problem. Min s.t. 4A + 7B 1A + 4B ≤ 21 2A + 1B27 3A +1.5B ≤ 21 -2A + 6B 20 A, B ≥ 0 (a) Find the optimal solution using the graphical solution procedure and the value of the objective function. at (A, B) = (b) Determine the amount of slack or surplus for each constraint. slack for 1A + 4B ≤ 21 surplus for 2A + 1B ≥ 7 slack for 3A + 1.5B ≤ 21 surplus for -2A + 6B ≥ 0 (c) Suppose the objective function is changed to max 8A + 3B. Find the optimal solution and the value of the objective function. at (A, B) =
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Objective Functions and Constraints:
Based on the given details, the objective functions and constraints are
Objective Function:
Constraints:
Subject to
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- Briefly explain these terms:a. Basic variableb. Shadow pricec. Range of feasibilityd. Range of optimalityAssuming that the company is interested in maximizing the total profit contribution, answer the following: A, What is the linear programming model for this problem? Decision Variables: LP Model: B.Find the optimal solution using the graphical solution procedure. 1.Feasible Region:2. Identify the binding constraint/s:3. Identify the rebundant constraint/s:4.How many gloves of each model should Kelson manufacture?5.What is the total profit contribution Kelson can earn with the given production quantities? C.How many hours of production time will be scheduled in each department? D.What is the slack time in each department? E.Compute the range of optimality for the objective function coefficientsQ2 Q2: For the following LP model, find values of the first iteration tableau variables using simplex method, in case that A is selected as .an entering variable Q2 Consider the following linear programming problem: Max 3A + 3B s.t. 2A + 4B ≤ 12 6A + 4B ≤ 24 A, B ≥ 0
- Asap ppz Three electricity generating firms are competing in the market with the inverse demand given by P[Q) = 21-Q. All firms have constant marginal costs. Firm 1's marginal cost is MC=5; it has a capacity constraint of K1= 5 units. Firm 2's marginal cost is MC 8; it has a capacity constraint of K2 = 3 units. Firm 3's marginal cost is MC = 10; it has a capacity constraint of K3= 3 units.A. The three firms compete in the style of Cournot. Please compute the Nash equilibrium quantities. Also compute the price in the Nash equilibrium.B. Which of these firms would have produced a larger quantity if it had a larger capacity? Please explain.1. If constraint has a shadow price of $6, Right-Hand-Side (RHS) is 12, allowable increase is 2, allowable decrease is 4. How would objective function change if the RHS of this constrains changes from 12 to 9? Answer___________Define the term constraint.
- Variable Cells Model Variable W M Constraints Constraint Number 1 2 3 Name Westem Foods Salsa Mexico City Salsa Name Whole tomatoes Tomato sauce Tomato paste Final Value 560.000 240.000 Reduced Objective Cost Coefficient 0.000 1.000 0.000 1.250 Shadow Price Final Value 4480,000 1920,000 1600,000 0.188 0.125 0,000 Constraint R.H. Side 4480.000 2080.000 1600,000 Allowable Increase 0.250 0.150 Allowable Increase 1120.000 1E+30 40,000 Allowable Decrease 0.107 0.250 Allowable Decrease 160.000 160,000 320.000 Analyze the sensitivity report shown above- a. What is the optimal solution and what are the optimal production quantities? b. Specify the objective coefficient ranges. c. What are the shadow prices for each constraint? Interpret each. d. Identify each of the right-hand-side rangesFormulate an LP model for the following problems.1. Bernadette intends to invest up to ₱50,000 in either Best Fund, or a time deposit orboth. The Best Fund pays 8% per year and the time deposit pays 9%. Because theBest Fund is riskier than the time deposit, so she intends to put at most ₱30,000 intothe time deposit and at least ₱10,000 into the Best Fund. How much should she allotto each investment in order to maximize her returns?what is the shawdow price of constraint 1?
- b) The Scott Tractor Company ships tractor parts from Omaha to St. Louis by railroad. However, a contract limits the number of railroad cars the company can secure on each branch/arc during a week. Given these limiting conditions, the company wants to know the maximum number of railroad cars containing tractor parts that can be shipped from Omaha to St. Louis during a week. Phoenix Des Moines 3 5 6. 6. 1. Dallas 2 Omaha St. Louis 7. 3 Denver 6. ActivateW O 31°CPleaseVariable Cells Model Variable Constraints E S D Constraint Number 1 E 2 3 S D S D Name Economy Models Standard Models Deluxe Models Name Total Profit: $ Fan Motors Cooling Coils Manufacturing Time Optimal Solution Constraints Fan motors Cooling coils Final Value 80.000 120.000 0.000 Final Value 200.000 320.000 2080.000 a. Identify the range of optimality for each objective function coefficient. If there is no lower or upper limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place. Objective Coefficient Range Variable lower limit upper limit E Reduced Cost 0.000 0.000 -24.000 Manufacturing time. AUTO Shadow Price 31.000 32.000 0.000 Right-Hand-Side-Range lower limit upper limit Objective Coefficient 63.000 95.000 135.000 b. Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. What will the new optimal…