earchThe production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (5). Two resources are constrained: production time (T), of whichshe has at most 12 hours per day, and carbonated water (W), of which she can get at most 1,500 gallons per day. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while acase of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. What is the production timeconstraint (in minutes)?Multiple Choice5R-5S-7203R-25 7203R-55 7202R-55 7202R-3S≤7202< Prev23 of 38Next >77°F Windy

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Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 111P

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The 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.
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Cara Ryder manages a ski school in a large resort and is try-ing to develop a schedule for instructors. The instructorsreceive little salary and work just enough to earn room andboard. They receive free skiing and spend most of their freetime tackling the resort’s notorious double black-diamondslopes. Hence, the instructors work only 4 days a week. Oneof the lesson packages offered at the resort is a 4-day begin-ner package. Ryder likes to keep the same instructor with agroup over the 4-day period, so she schedules the instructorsfor 4 consecutive days and then 3 days off. Ryder uses years ofexperience with demand forecasts provided by managementto formulate her instructor requirements for the upcomingmonth.a. Determine how many instructors Ryder needs to employ.Give preference to Saturday and Sunday off. (Hint: Lookfor the group of 3 days with the lowest requirements.)b. Specify the work schedule for each employee. How muchslack does your schedule generate for each day?
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The Ace Manufacturing Company has orders for three similar products. Product A Min B C 1 2 Machine 3 Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are shown below. A A B B Ic C Product 1 12 3 Orders (units) 1,900 500 1,100 Capacity (units) 1,300 1,600 800 1 Machine 2 3 $1.00 $1.30 $1.10 $1.20 $1.40 $1.00 $0.90 $1.20 $1.20 (a) Develop the linear programming formulation of this problem. (Let XA1 be the number of units of product A produced by machine 1, X;; be the number of units of product i produced by machine j, etc.)
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A 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?
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Tuff-Rider, Inc., manufactures touring bikes and mountain bikes in a variety of frame sizes, colors, and component combinations. Identical bicycles are produced in lots of 110. The projected demand, lot size, and time standards are shown in the following table: Item Touring Mountain Demand forecast 4,000 units/year 12,000 units/year Lot size 100 units 110 units Standard processing time 0.25 hour/unit 0.50 hour/unit Standard setup time 2 hours/lot 3 hours/lot The shop currently works 8 hours a day, 5 days a week, 52 weeks a year. It operates five workstations, each producing one bicycle in the time shown in the table. The shop maintains a 15 percent capacity cushion. How many workstations will be required next year to meet expected demand without using overtime and without decreasing the firm's current capacity cushion? The number of workstations required next year is ?(Enter your response rounded up to the next whole number.)
The XYZ company produces all type of office furniture. The “Executive Secretary” is a chair that has been designed using ergonomics to provide comfort during long office hours. The chair sells for $130. There are 480 minutes available during the day, and the average daily demand has been 50 chairs. There are eight tasks; Task Time (min) Immediate predecessor A 4 - B 7 - C 6 A, B D 5 C E 6 D F 7 E G 8 E I 6 F, G a) Draw a precedence diagram of this operation b) What is the cycle time for this operation? c) What is the theoretical minimum number of workstations? d) Assign tasks to the workstations e) What is the idle time per cycle? f) What is the efficiency of the assembly line?

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