Max −A + 2B s.t. -2A + 3B ≤ 8 (Constraint 1) 6A - 2B ≤ 5 (Constraint 2) A + B ≤ 5 (Constraint 3) A ≥ 1 (Constraint 4) A, B ≥ 0 SHOW ALL CALCULATION STEPS a) Solve the LP Model using the graphical method. Label your graph completely (and upload your graph as a jpg). State your optimal solution and objective function value. b) Calculate the Slack/Surplus for each constraint. c) Calculate the Shadow/dual Prices for each constraint.
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Max |
−A + 2B |
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s.t. |
-2A + 3B ≤ 8 (Constraint 1) |
|
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6A - 2B ≤ 5 (Constraint 2) |
|
|
A + B ≤ 5 (Constraint 3) A ≥ 1 (Constraint 4) |
|
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A, B ≥ 0
|
SHOW ALL CALCULATION STEPS
a) Solve the LP Model using the graphical method. Label your graph completely (and upload your graph as a jpg). State your optimal solution and objective function value.
b) Calculate the Slack/Surplus for each constraint.
c) Calculate the Shadow/dual Prices for each constraint.
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- If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.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___________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☆
- Company aims to determine the optimal number of products to be produced in order to maximize the total profit. a) Formulate the problem using algebraic method. b) Solve the model using the graphical method (indicate optimal solution and profit). C) again). Use graphical method to determine the shadow price for each of these resources (based on the definition of shadow price and by increasing each resource by one unit and solving the problem d) Use the Excel solver to do parts b and c. e) follow: Using Solver Table generate the optimal solution and the total profit for each resource as e1: Consider unit profit for product 1 (use range from 0 to 4 and increment of 1) e2: Consider unit profit for product 2 (use range from 0 to 4 and increment of 1) е3: Consider simultaneous changes for both unit profits in part e1 and e2 using given ranges. e4: Consider available resource of Raw material 1 (use range from 2 to 14 and increment of 1) e5: Consider available resource of Raw material 2 (use…Elaborate/ Explain Integer Linear Optimization and put examplesLPP 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 )
- 2. A distillery makes three kinds of authentic Philippine wine: Sweet, Regular, and Extra Dry. The raw materials, labor, and profit for a gallon of each wine are summarized below: Wines Sweet Regular Extra Dry Grapes Grade A (bushels) 3 5 2 Grapes Grade B (bushels) 2 2 1 Sugar (pound) 2 1 2 Labor (hours) 2 4 2 Profit per Gallon Php 350 Php 400 Php 450 If the winery has 200 bushels of Grade A grapes, 160 bushels of Grade B grapes, 120 pounds of sugar, and 300 labor hours available during the next week, what product mix of wine will maximize the company profit? Linear Program:Please answer it immediately sir Linear Programming The Booboo sawmill in Batangas produces pine and oak boards for manufacturing firms. Each month the sawmill must deliver atleast 5 tons of wood to the manufacturer . It takes the sawmill 3 days to produce a ton of pine and a 2 days to produce a ton of oak and the sawmill can allocate 18 days out of a month for this contract. The sawmill can get enough pine to make atleast 4 tons of wood and enough oak to make atmost 7 tons of wood. Determine the number of tons of pine and oak in order to minimize cost, given that pine has a cost of $3 and oak $6 to produceIncrease the amount of special sauce available by 1 ounce and re-solve. Does the solution confirm the answer to part (c)? Give the new solution.
- What is the fertilizer constraint? a. 2r t c <= 10 b. r + c <= 10 c. 3r + 3c <= 10 d. none of the aboveQ1. 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 7-41 Southern Oil Company produces two grades of gasoline: regular and premium. The profit contributions are $0.30 per gallon for regular gasoline and $0.50 per gallon for premium gasoline. Each gallon of regular gasoline contains 0.3 gallons of grade A crude oil and each gallon of premium gasoline contains 0.6 gallons of grade A crude oil. For the next production period, Southern has 18,000 gallons of grade A crude oil available. The refinery used to produce the gasolines has a production capacity of 50,000 gallons for the next production period. Southern Oil's distributors have indicated that demand for the premium gasoline for the next production period will be at most 20,000 gallons. a. Formulate linear programming model that can be used to determine the number of gallons of regular gasoline and the number of gallons of premium gasoline that should be produced in order to maximize tota profit contribution. If required, round your answers to two decimal places. L Let R = P =…