Bangs Leisure Chairs produces three types of hand-crafted outdoor chairs: sling chairs, Adirondack chairs, and hammocks. After reviewing the labor required for each type of chair, the followinglinear optimization model for profit was found, where S is the number of sling chairs produced, A is the number of Adirondack chairs produced, and H is the number of hammocks 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 integersolution objective function and the linear optimization solution objective function? Would rounding the continuous solution have provided the optimal integer solution?Maximize Profit=40 S + 95 A + 90 H0.6 S + 2 A+ 0.5 H ≤ 400.75 S + 2 A + 3 H ≤ 40S+A+H≤ 402.35 S +5 A + 4.5 H≤ 95S, A, H20(Hours cutting ≤ 40)(Hours assembly ≤ 40)(Hours finishing ≤40)(Total hours/month ≤ 95)(Nonnegativity)The optimal integer solution is to produce sling chair(s), Adirondack chair(s), and(Type whole numbers.)hammock(s). This solution gives theprofit, which is $The absolute value of the difference between the optimal integer solution objective function and the linear optimization solution objective function is $ Rounding the continuous solutionhave provided the optimal integer solution.(Type integers or decimals rounded to two decimal places as needed.)

Linear programming (LP) is a mathematical optimization technique that helps solve problems where an…

Answered: The optimal integer solution is to…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section: Chapter Questions

Problem 46P

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Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?
Valencia products makes automobile radar detectors and assembles two models. Laser stop 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 = 123 L + 139 S 19 L + 11 S < 4,000 (availability of component A) 6 L + 9 S < 35000 (availability of component B) L > 0 and S > 0 The optimal solution is to produce how many Laser stop models ? And how many Speedbuster models ? The maximum possible profit is ? Component A is or is not a binding…
Explain why satisficing exists and why someone would not require an optimal solution.
Suppose the following costs for a 10-hour round-trip flight apply to the time frame and expenses of an unscheduled 5-hour charter flight from Baltimore to Las Vegas (and return the next day) on a seven-year-old Boeing 737–800 with 120 occupied seats. Some costs listed in the table have been aggregated up to the flight level from a seat-level decision where they are incurred. Others have been allocated down to the flight level from an entry/exit or maintain-ownership company-level decision. Still other costs vary with the go/no go flight-level decision itself. Your job is to analyze each cost item and figure out the “behavior of cost”—that is, with which decision each cost varies. Fuel and landing fees =$5,200 Quarterly airframe maintenance re: FAA certificate = $1,000 Unscheduled engine maintenance per 10 flight hours =$1,200 Pro rata time depreciation for seventh year of airframe = $7,200 Flight pay for pilots per round-trip flight = $4,200 Long-term hangar facility lease = $6,600…
Hudson Corporation is considering three options for managing its data processing operation: continuing with its own staff, hiring an outside vendor to do the managing (referred to as outsourcing), or using a combination of its own staff and an outside vendor. The cost of the operation depends on future demand. The annual cost of each option (in thousands of dollars) depends on demand as follows: Demand Staffing Options High Medium Low Own staff 650 650 600 Outside vendor 900 600 300 Combination 800 650 500 If the demand probabilities are 0.2, 0.5, and 0.3, which decision alternative will minimize the expected cost of the data processing operation? What is the expected annual cost associated with that recommendation? Expected annual cost = $fill in the blank 2 Construct a risk profile for the optimal decision in part (a). The input in the box below will not be graded, but may be reviewed and considered by your instructor.
Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here: Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 Hours required to complete all the oak cabinets 50 44 32 Hours required to complete all the cherry cabinets 61 46 34 Hours available 35 25 30 Cost per hour $36 $43 $56 For example, Cabinetmaker 1 estimates that it will take 50 hours to complete all the oak cabinets and 61 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 35 hours available for the final…
Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here: Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 Hours required to complete all the oak cabinets 47 40 27 Hours required to complete all the cherry cabinets 64 51 36 Hours available 40 30 35 Cost per hour $34 $41 $52 For example, Cabinetmaker 1 estimates it will take 47 hours to complete all the oak cabinets and 64 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 40 hours available for the final…
c. If Cabinetmaker 1 has additional hours available, would the optimal solution change? If required, round your answers to three decimal places. If your answer is zero, enter "0". Explain. ✓ because Cabinetmaker 1 has dual value Yes ✓ of No -1.84 ✔ ✓ of Therefore, each additional hour of time for cabinetmaker 1 will reduce total cost by $ d. If Cabinetmaker 2 has additional hours available, would the optimal solution change? If required, round your answers to three decimal places. If your answer is zero, enter "0". Use a minus sign to indicate the negative figure. Explain. ✔ because Cabinetmaker 2 has a slack 1.84 ✔ per hour, up to a maximum of 30 X hours. Alternatively, the dual value is 50 ✓ hours. 0.00 ✓ which means that adding one hour to this constraint will decrease total cost by $ 0.00 ✓.
Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here: Hours required to complete all the oak cabinets Hours required to complete. all the cherry cabinets Hours available Cost per hour Min s.t. 01 Let O₁ O₂ 01 01 For example, Cabinetmaker 1 estimates it will take 50 hours to complete all the oak cabinets and 60 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 40 hours available for the final finishing operation. Thus, Cabinetmaker 1 can only complete 40/50 = 0.8, or 80%,…
Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here: Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 Hours required to complete all the oak cabinets 50 44 32 Hours required to complete all the cherry cabinets 61 46 34 Hours available 35 25 30 Cost per hour $36 $43 $56 For example, Cabinetmaker 1 estimates that it will take 50 hours to complete all the oak cabinets and 61 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 35 hours available for the final…
The Rotary Club is holding a pizza sale to finance outreach projects. The Club made an agreement to purchase pizza from Pizza Hut at a 30% discount which the Rotary Club can thên resell for a profit. It is expected that of the 500 families in the community, at most 70% will buy Pizza. Based on a survey of their personal preferences, the students believe that they should order no more than 120 cheese pizzas, no more than 150 pepperoni pizzas, and no more than 100 vegetarian pizzas. They also want to make sure that at least 20% of the total pizzas are cheese and at least 50% of the pizzas are pepperoni. The standard price (before discount) for the cheese, pepperoni and vegetarian is $12, $15 and $14, respectively. The Rotary Club makes a profit of 10%, 15% and 20%, respectively, for each cheese, pepperoni, and vegetarian pizza they resell Formulate a linear programming model that would determine the optimal solution.
HERO Corporation is considering three options for managing its data processing operation: continuing with its own staff, hiring an outside vendor to do the managing (referred to as outsourcing), or using a combination of its own staff and an outside vendor. The cost of the operation depends on future demand. The annual cost of each option (in thousands of pesos) depends on demand as follows: Demand Demand Demand Staffing Options High Medium Low Own staff 352 325 300 Outsider vendor 450 300 150 Combination 400 325 250 If the decision maker knows nothing about the probabilities of the four states of nature, what is the recommended decision using:i. the optimistic approach and the conservative approach iii. the minimax regret approach iv. the Laplace method

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