2. Min Z = 5x₁ + x₂subject to2x₁ +x₂ ≥ 6x₁ +X₂ ≥ 42x₁ + 10x₂ ≥ 20X1, X₂ ≥ 0a) Solve the LP model using the graphical method and determine the optimalsolution.b) Calculate slack/surplus for each constraint.c)If the RHS of constraint 1 increases by 1, by how much would the objectivefunction value change?d) If the RHS of constraint 2 increases by 1, by how much would the objectivefunction value change?

To solve the LP model using the graphical method, we first plot the feasible region determined by…

Answered: a) Solve the LP model using the…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Problem 2: Applications of Linear Programming: Visa Inc. Stock sells for $92 a share and has 3-year average annual return of $20 a share. The beta value is 1.06. JP Morgan Chase and Co. sells for $87 a share and has a 3-year average annual return of $17 a share. The beta value is 1.21. Derek wants to spend no more than $15,000 investing in these two stocks, but he wants to earn at least $2500 in annual revenue. Derek also wants to minimize the risk. Determine the number of shares of each stock that Derek should buy.
The DellaVecchia Garden Center purchases and sells Christmas trees during the holiday season. It purchases the trees for $10 each and sells them for $20 each. Any trees not sold by Christmas day are sold for $2 each to a company that makes wood chips. The garden center estimates that four levels of demand are possible: 100, 200, 500, and 1,000 trees.a. Compute the payoffs for purchasing 100, 200, 500, or1,000 trees for each of the four levels of demand.b. Construct a payoff table, indicating the events and alternative courses of action.c. Construct a decision tree.d. Construct an opportunity loss table. Use the Optimistic (maximax) to choose the best choice.e.Use the Pessimistic (maximin) to choose the best choice.f.Use the Criterion of realism (Hurwicz) to choose the best choice. α = 0.6g.Use the Equally likely (Laplace) to choose the best choice.h.Use the Minimax regret to choose the best choice.i.Use the expected monetary value to make a choice. ( Probability for the four level…
The DellaVecchia Garden Center purchases and sells Christmas trees during the holiday season. It purchases the trees for $10 each and sells them for $20 each. Any trees not sold by Christmas day are sold for $2 each to a company that makes wood chips. The garden center estimates that four levels of demand are possible: 100, 200, 500, and 1,000 trees.a. Compute the payoffs for purchasing 100, 200, 500, or1,000 trees for each of the four levels of demand.b. Construct a payoff table, indicating the events and alternative courses of action.c. Construct a decision tree.d. Construct an opportunity loss table. Use the Optimistic (maximax) to choose the best choice.e.Use the Pessimistic (maximin) to choose the best choice.f.Use the Criterion of realism (Hurwicz) to choose the best choice. α = 0.6g.Use the Equally likely (Laplace) to choose the best choice. h.Use the Minimax regret to choose the best choice.i.Use the expected monetary value to make a choice. ( Probability for the four level…
A retail has 8 stores supplied from 4 suppliers, where each supplier supplies different goods. Delivery from the Supplier is in trucks with a capacity of 40,000 units at a cost of $1100 per load plus $100 per delivery to the store. Inventory costs are $0.2 per unit per year. The Supply Chain Manager is considering whether to use direct shipping or Milk Run delivery for 4 stores for each truck in one shipment a) if annual sales in each store are 1000,000 units, which shipping method provides the lower cost b) if the annual sales in each store are 200,000 units, which shipping method provides the lower cost
Using Excel Solve the following LP Maximize $4x + $5y Subject to 2x + 3y ≤ 20 (labor, in hours) 6x + 6y ≤ 36 (materials, in pounds) 4x + 4y ≤ 40 (storage, in square feet) x, y ≥ 0 a) Write the original optimal solution and objective function value. b) What is the optimal solution and objective function value if you acquire 2 additional pounds of material? c) What is the optimal solution and objective function value if you acquire 1.5 additional hours of labor?
How would you write the optimal solution for these?
Friendly Waste Co. runs three different factories and is required by law to safely dispose of chemicals. Waste from three different factories can be processed to reduce the amount of two different types of pollutants. State law requires that the total reduction in the amount of pollutant A is at least 30 tons and pollutant B is at least 40 tons. Using the information in the following table: Factory Proc Cost Per Ton Reduction Plant A Reduction Plant B 1 15 0.1 0.45 2 10 0.2 0.25 3 20 0.4 0.3 •Algebraically formulate a linear programming model to represent this problem.
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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 =…
Variable 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…
Using Goal Seek for the following problem, how much is needed for John to deposit each year into an account to save $5,000 for his new Specialized Mountain bike. Assumes both deposit and withdrawal are at beg of each year Deposit = Interest= Yr 0 Yr 1 Yr 2 Beg Balance $0.00 $0.00 $0.00 Deposit $0.00 $0.00 -$5,000.00 Interest Earned 8% $0.00 $0.00 na End Balance $0.00 $0.00 -$5,000.00

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