Concept explainers
Cara Ryder manages a ski school in a large resort and is trying to develop a
- Determine how many instructors Ryder needs to employ. Give preference to Saturday and Sunday off. (Hint: Look for the group of 3 days with the lowest requirements.)
- Specify the work schedule for each employee. How much slack does your schedule generate for each day?
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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?arrow_forwardThe Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.arrow_forwardAssume 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.arrow_forward
- A small candy shop is preparing for the holiday season. The owner must decide how many bags of deluxe mix and how many bags of standard mix of Peanut/Raisin Delite to put up. The deluxe mix has 2/3 pound raisins and 1/3 pound peanuts, and the standard mix has 1/2 pound raisins and 1/2 pound peanuts per bag. The shop has 90 pounds of raisins and 60 pounds of peanuts to work with. Peanuts cost $.60 per pound and raisins cost $1.50 per pound. The deluxe mix will sell for $4.00 for a one-pound bag, and the standard mix will sell for $3.55 for a one-pound bag. The owner estimates that no more than 210 bags of one type can be sold. a. If the goal is to maximize profits, how many bags of each type should be prepared? Deluxe _____bags Standard ______bags b. What is the expected profit? Profit ________arrow_forwardThe Grand Valley Company, run by the J. Motwani family, produces two products: bed mattresses and box springs. A prior contract requires that the firm produce at least 30 mattresses or box springs, in any combination, per week. In addition, union labor agreements demand that stitching machines be kept running at least 40 hours per week, which is one production period. The firm plans to purchase four machines. Each box spring takes 2 hours of stitching time, while each mattress takes 1 hour on the machine. The firm believes that it can sell at least twice as many mattresses as box springs. Each mattress produced cost $20 and each box spring costs $24. Formulate this problem as a linear programming problem. Summarize the information in this problem into a table similar to table 1, page 701. Formulate the problem as a linear programming problem ( i.e., Write the standard mathematical format).arrow_forwardA small candy shop is preparing for the holiday season. The owner must decide how many bags ofdeluxe mix and how many bags of standard mix of Peanut/Raisin Delite to put up. The deluxe mixhas 2⁄3 pound raisins and 1⁄3 pound peanuts, and the standard mix has 1⁄2 pound raisins and 1⁄2 poundpeanuts per bag. The shop has 90 pounds of raisins and 60 pounds of peanuts to work with.Peanuts cost $.60 per pound and raisins cost $1.50 per pound. The deluxe mix will sell for $2.90for a one-pound bag, and the standard mix will sell for $2.55 for a one-pound bag. The owner estimates that no more than 110 bags of one type can be sold.a. If the goal is to maximize profits, how many bags of each type should be prepared?b. What is the expected profit?arrow_forward
- A brewery produces regular beer and a lower-carbohydrate Tight beer. Steady customers of the brewery buy 12 units of regular beer and 16 units of light beer monthly. While setting up the brewery to produce the beers, the management decides to produce extra beer, beyond that needed to satisfy customers. The cost per unit of regular beer is $32,000 and the cost per unit of light beer is $60,000. Every unit of regular beer brings in $100,000 in revenue, while every unit of light beer brings in $300,000 in revenue. The brewery needs at least $9,000,000 in revenue, and has determined that the total demand will be at least 50 units of beer. Complete parts (a) and (b).arrow_forwardNoah Yobs, who has $75,400 of AGI (solely from wages) before considering rental activities, has $67,860 of losses from a real estate rental activity in which he actively participates. He also actively participates in another real estate rental activity from which he has $37,700 of income. He has other passive activity income of $24,128. a. What amount of rental loss can Noah use to offset active or portfolio income in the current year? 6,032 Compute Noah’s AGI on Form 1040 [pages 1 and 2; also complete Schedule 1 (Form 1040)] for the current year. Use the minus sign to indicate a loss.arrow_forwardA company with a capacity of 3,000 units a month has fixed costs of P1,500 a month and labor costs of P10 a unit. Material costs are P5 per unit. The company has been producing at 80 percent of capacity and selling its product for P20. 1What would its net income be at 100 percent at capacity 1.2What would its net income be at 120 percent of capacity if it is assumed that 20 percent more products could be produced on overtime at an extra P3 labor cost per unit for all production above 100 percent?arrow_forward
- Hi can I get help on this please? I am stuck!! Question: lumber and plywood. In a given week, the mill can turn out 400 units of production, of which at least 100 units of lumber and at least 150 units of plywood are required by regular customers. The profit is $25 per unit of lumber and $38 per unit of plywood. Assume that all units produced are sold. How many units of each should the mill produce in order to maximize the profit? What is the maximum profit?arrow_forwardNature's Garden Inc. produces wood chips, wood pulp, and mulch. These products are produced through harvesting trees and sending the logs through a wood chipper machine. One batch of logs produces 20,304 cubic yards of wood chips, 14,100 cubic yards of mulch, and 9,024 cubic yards of wood pulp. The joint production process costs a total of $32,000 per batch. After the split-off point, wood chips are immediately sold for $25 per cubic yard while wood pulp and mulch are processed further. The market value of the wood pulp and mulch at the split-off point is estimated to be $22 and $24 per cubic yard, respectively. The additional production process of the wood pulp costs $5 per cubic yard, after which it is sold for $30 per cubic yard. The additional production process of the mulch costs $4 per cubic yard, after which it is sold for $32 per cubic yard.arrow_forwardTiny Toy Company makes three types of new toys: the tiny tank, the tiny truck, and the tiny turtle. Plastic used in one unit of each is 1.5, 2.0 and 1.0 pounds, respectively. Rubber for one unit of each toy is 0.5, 0.5, and 1.0 pounds, respectively. Also, each tank uses 0.3 pounds of metal, and the truck uses 0.6 pounds of metal during production. The average weekly availability for plastic is 16,000 pounds, 9,000 pounds of metal, and 5,000 pounds of rubber. It takes two hours of labor to make one tank, two hours for one truck, and one hour for a turtle. The company allows no more than 40 hours a week for production (priority #1). Finally, the cost of manufacturing one tank is $7, 1 truck is $5 and 1 turtle is $4; a target budget of $164,000 is initially used as a guideline for the company to follow. Minimize over-utilization of the weekly available supply of materials used in making the toys and place twice as much emphasis on the plastic (priority #2) I understand…arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,