Write the mathematical model and use Solver sensitivity analysis to answer the following question: A farm co-op has 6,001 acres available to plant with corn and soybeans. Each acre of corn requires 9 gallons of fertilizer/herbicide and 0.75 hour of labor to harvest. Each acre of soybeans requires 3 gallons of fertilizer/herbicide and 1 hour of labor to harvest. The co-op has available at most 40,500 gallons of fertilizer/herbicide and at most 5,250 hours of labor for harvesting. Find the shadow price associated with the "fertilize/herbicide" constraint if the profits per acre are $65 for corn and $45 for soybeans. Round your answer to the nearest cent if necessary. A$0.00 B$1.11 C$2.22 D$3.33 E$4.44

Write the mathematical model and use Solver sensitivity analysis to answer the following question: A farm co-op has 6,001 acres available to plant with corn and soybeans. Each acre of corn requires 9 gallons of fertilizer/herbicide and 0.75 hour of labor to harvest. Each acre of soybeans requires 3 gallons of fertilizer/herbicide and 1 hour of labor to harvest. The co-op has available at most 40,500 gallons of fertilizer/herbicide and at most 5,250 hours of labor for harvesting. Find the shadow price associated with the "fertilize/herbicide" constraint if the profits per acre are $65 for corn and $45 for soybeans. Round your answer to the nearest cent if necessary. A$0.00 B$1.11 C$2.22 D$3.33 E$4.44

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter10: Introduction To Simulation Modeling

Section: Chapter Questions

Problem 35P: Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season....

See similar textbooks

Similar questions

Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.
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?
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
Lou Silva has owned and operated The Wellness Store for fifteen years. The company's year-end is December 31st. The following chart lists the company's assets owned prior to 2021 and their UCC balances at the end of 2020. Asset UCC Balance Store (building purchased in 2005) $100,000 Delivery van (Class 10) 15,000 Furniture and office equipment (Class 8) 30,000 Photocopier purchased in 2019 (Separate Class 8) 2,000 Patent (purchased in 2018) 10,000 The following transactions took place in 2021: a. Lou purchased $2,000 worth of small tools (each costing under $500). b. The delivery van was sold for $12,000. The original cost was $20,000. A second-hand van was purchased in the year for $16,000. c. $15,000 was paid for an air conditioning system in the building, which was added to the cost of the standard Class 1 pool. d. Lou sold the photocopier for $1,500 in the year, and will replace it in January 2022 with a second-hand model valued…
In the past, Peter Kelle's tire dealership in Baton Rouge sold an average of 1,000 radials each year. In the past 2 years, 240 and 240, respectively were sold in fall, 350 and 320 in winter,150 and165 in spring, and 340 and 195 in summer. With a major expansion planned, Kelle projects sales next year to increase to 1,200 radials. Based on next year's projected sales, the demand for each season is going to be (enter your responses as whole numbers): Fall: Winter: Spring: Summer:
The Fish House (TFH) in Norfolk, Virginia, sells fresh fish and seafood. TFH receives daily shipments of farm-raised trout from a nearby supplier. Each trout costs $2.45 and is sold for $3.95. To maintain its reputation for freshness, at the end of the day TFH sells any leftover trout to a local pet food manufacturer for $1.25 each. The owner of TFH wants to determine how many trout to order each day. Historically, the daily demand for trout is: Demand 10 11 12 13 14 15 16 17 18 19 20 Probability 0.02 0.06 0.09 0.11 0.13 0.15 0.18 0.11 0.07 0.05 0.03 a. Construct a payoff matrix for this problem. b. How much should the owner of TFH be willing to pay to obtain a demand forecast that is 100% accurate? give a clear explanation for (b)
HMO has 40 doctors to be apportioned among four clinics. The HMO decides to apportion the doctors based on the average weekly patient load for each clinic, given in the following table. Clinic A B C D Average Weekly 275 392 611 724 Patient Load Find the apportion of A and C using using Adam's Method. Use modified divisor 52. Doctors for clinic A Doctors for clinic B = %3D Doctors for clinic C= Doctors for clinic D =
The world's oceans contain on average of 0.9 oz of Au /ton of ocean water. There were 2 proposed novel process in mineral extraction to recover the Au and they were compared using Engineering Economic Analysis. Process X costs $600/ton of ocean water processed and a recovery of 90%, while Process Z costs $450/ton and a recovery of 60%. Both processes will need the same amount of capital investment and equal ounces of Au extracted daily. If the Au today is $2,200/oz, which process is more feasible considering the fact that the world's ocean can be inexhaustible? This problem requires the analysis to be on the basis of profit per ounce of Au extracted.
At a small but growing airport, the local airline company is purchasing a new tractor for a tractor-trailer train to bring luggage to and from the airplanes. A new mechanized luggage system will be installed in 3 years, so the tractor will not be needed after that. However, because it will receive heavy use, so that the running and maintenance costs will increase rapidly as the tractor ages, it may still be more economical to replace the tractor after 1 or 2 years. The following table gives the total net discounted cost associated with purchasing a tractor (purchase price minus trade-in allowance, plus running and maintenance costs) at the end of year i and trading it in at the end of year j (where year O is now). i 012 1 $13,000 j 2 $28,000 $17,000 3 $48,000 $33,000 $20,000 The problem is to determine at what times (if any) the tractor should be replaced to minimize the total cost for the tractors over 3 years. (a) Formulate this problem as a minimum cost flow problem by showing the…
Western Chassis produces high-quality polished steel and aluminum sheeting and two lines ofindustrial chassis for the rack mounting of Internet routers, modems, and other telecommunicationsequipment. The contribution margin (contribution toward profit) for steel sheeting is $0.40 per poundand for aluminum sheeting is $0.60 per pound. Western earns $12 contribution on the sale of aStandard chassis rack and $15 contribution on a Deluxe chassis rack. During the next productioncycle, Western can buy and use up to 25,800 pounds of raw unfinished steel either in sheeting or inchassis. Similarly, 20,400 pounds of aluminum are available. One standard chassis rack requires 16pounds of steel and 8 pounds of aluminum. A Deluxe chassis rack requires 12 pounds of each metal.The output of metal sheeting is restricted only by the capacity of the polisher. For the next productioncycle, the polisher can handle any mix of the two metals up to 4,000 pounds of metal sheeting. Chassismanufacture can be…
Please show solution and formula used. Assuming the total number of students studying in the top four universities in the Philippines is approximately 158,000. And the distribution is as follows: University of the Philippines (UP) - 40% of the total number Ateneo de Manila University (ADMU) - 23,700 De La Salle University (DLSU) - 25% of the total number University of Santo Tomas - 20% of the total number And only the following number of students owns a tablet computer: 20% of UP students 85% of ADMU students 90% of DLSU students 85% of UST students What is the total market penetration of tablet computers among the students of the top four universities? What is the total market size of tablet computers in the top four universities?
At a small but growing airport, the local airline company is purchasing a new tractor for a tractor-trailer train to bring luggage to and from the airplanes. A new mechanized luggage system will be installed in 3 years, so the tractor will not be needed after that. However, because it will receive heavy use, so that the running and maintenance costs will increase rapidly as the tractor ages, it may still be more economical to replace the tractor after 1 or 2 years. The following table gives the total net discounted cost associated with purchasing a tractor (purchase price minus trade-in allowance, plus running and maintenance costs) at the end of year i and trading it in at the end of year j (where year O is now). i B 012 1 $13,000 j 2 $28,000 $17,000 3 $48,000 $33,000 $20,000 The problem is to determine at what times (if any) the tractor should be replaced to minimize the total cost for the tractors over 3 years. (a) Formulate this problem as a shortest-path problem by drawing a…