The Perth Mining Company operates two mines for thepurpose of extracting gold and silver. The Saddle Minecosts $14,000/day to operate, and it yields 50 oz ofgold and 3,000 oz of silver per day. The HorseshoeMine costs $16,000/day to operate, and it yields 75 ozof gold and 1,000 oz of silver per day. Companymanagement has set a target of at least 650 oz of goldand 18,000 oz of silver. You boss would like you tofocus on the following five issues: 1. How many daysshould each mine be operated so that the target can bemet at a minimum cost? 2. Find the range of valuesthat the Saddle Mine's daily operating cost can assumewithout changing the optimal solution. 3. Find therange of values that the requirement for gold and silvercan assume. 4. Find the shadow price for therequirement for gold and silver.

Linear programming helps us to find the optimal solution/best outcome, with the given constraints.We…

Answered: The Perth Mining Company operates two…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 63P: It costs a pharmaceutical company 75,000 to produce a 1000-pound batch of a drug. The average yield...

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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.
It costs a pharmaceutical company 75,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for the drug is unknown, with the best case being 20,000 pounds, the most likely case 17,500 pounds, and the worst case 10,000 pounds. The drug sells for 125 per pound and leftover amounts of the drug can be sold for 30 per pound. To maximize annual expected profit, how many batches of the drug should the company produce? You can assume that it will produce the batches only once, before demand for the drug is known.
The East Midvale Textile Company produces denim and brushed-cotton cloth. The average production rate for both types of cloth is 1,000 yards per hour, and the normal weekly production capacity (running two shifts) is 80 hours. The marketing department estimates that the maximum weekly demand is for 60,000 yards of denim and 35,000 yards of brushed cotton. The profit is $3.00 per yard for denim and $2.00 per yard for brushed cotton. The company has established the following four goals, listed in order of importance: (1) Eliminate underutilization of production capacity to maintain stable employment levels. (2) Limit overtime to 10 hours. (3) Meet demand for denim and brushed cotton weighted according to profit for each. (4) Minimize overtime as much as possible. a. Formulate a goal programming model to determine the number of yards (in 1,000-yard lots) to produce to satisfy the goals. b. Solve this model by using the computer.
The Toys-R-U Company has developed two new toys for possible inclusion in its product line for the upcoming Christmas season. Setting up the production facilities to begin production would cost $50,000 for toy1 and $80,000 for toy 2. Once these costs are covered, the toys would generate a unit profit of $10 for toy 1 and $15 for toy 2. The company has two factories that are capable of producing these toys. However, to avoid doubling the start-up costs, just one factory would be used, where the choice would be based on maximizing profit. For administrative reasons, the same factory would be used for both new toys if both are produced. Toy 1 can be produced at the rate of 50 per hour in factory 1 and 40 per hour in factory 2. Toy 2 can be produced at the rate of 40 per hour in factory 1 and 25 per hour in factory 2. Factory 1 and 2, respectively, have 500 hours and 700 hours of production time available before Christmas that could be used to produce these toys. It is not known…
The Star Youth Soccer Club helps to support its 20 boys’ and girls’ teams financially, primarily through the payment of coaches. The club puts on a tournament each fall to help pay its expenses. The cost of putting on the tournament is $8,000, mainly for development, printing, and mailing of the tournament The tournament entry fee is $400 per team. For every team that enters, it costs the club about $75 to pay referees for the three-game minimum each team is guaranteed. If the club needs to clear $60,000 from the tournament, how many teams should it invite?
The Gulf Coast Foundry is developing a long-range strategic plan for buying scrap metal for its foundry operations. The foundry can buy scrap metal in unlimited quantities from two sources, Atlanta (A) and Birmingham (B), and it receives the scrap daily in railroad cars. The scrap is melted down, and lead and copper are extracted for use in the foundry processes. Each railroad car of scrap from source A yields 1 ton of copper and 1 ton of lead and costs $10,000. Each railroad car of scrap from source B yields 1 ton of copper and 2 tons of lead and costs $15,000. If the foundry needs at least 21/2 tons of copper and at least 4 tons of lead per day for the foreseeable future, how many railroad cars of scrap should be purchased per day from Source A and Source B to minimize the long-range scrap metal cost?
the gulf coast foundry is developing a long range strategic plan for buying scarp metal for its foundry oprations the foundry can buy scrap metal in unlimited quantities from two sources, Atlanta(A) and Birmingham (B), and it receives the scrap daily in railroad cars. the scrap is melted down, and lead lead and copper are extracted for use in the foundry processes each railroad car of scrap from source A yields 1 ton of copper and 1 ton of lead and cost $10,000. each railroad car of scrap from source B yields 1 ton of copper and 2 tons of lead and costs $15,000, if the foundry needs at least 2 and a half tons of copper and at least 4 tons of lead per day for the foreseeable future, how many railroad cars of scrap should be ( purchased per day from source A and source B to minimize the long range scrap metal cost?
Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rod is $2,000, and the cost required to set up the production for the 6-cylinder connecting rod is $3,500. Manufacturing costs are $15 for each 4-cylinder connecting rod and $18 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line.Once the line has been set up, the weekly production capacities are 6,000 6-cylinder connecting rods and 8,000 4-cylinder connecting rods. Letx4 = the number of 4-cylinder connecting rods produced next week,x6 = the number of 6-cylinder connecting rods produced next week,s4 = 1 if the production line is set up to produce the 4-cylinder…
The College of Business at Tech is planning to begin an online MBA program. The initial start-up cost for computing equipment, facilities, coursedevelopment, and staff recruitment and development is $350,000. The college plans to charge tuition of $18,000 per student per year. However,the university administration will charge the college $12,000 per student for the first 100 students enrolled each year for administrative costs and itsshare of the tuition payments. The college believes it can increase tuition to $24,000, but doing so would reduce enrollment to 35. Should the college consider doing this?
Easyville University awarded scholarships of $50,000.00 each to two students for a bachelor’s degree program. The standard time for degree completion is four years or 8 semesters. Easyville University stipulates that the scholarship amount will be increased or decreased depending on how well the students meet, exceed or fail to meet the standard time (i.e. more money for exceeding standard and less for failing to meet standard). Sam Speedy completed his degree program in three and one half years; while Larry Laggard completed his degree program in five years. Using the Standard Hour Plan, how much scholarship money will be given to: a)Speedy Sam? b) Larry Laggard?
The Wearever Carpet Company manufactures two brands of carpet—shag and sculptured— in 100-yard lots. It requires 8 hours to produce one lot of shag carpet and 6 hours to produce one lot of sculptured carpet. The company has the following production goals, in prioritized order: (1) Do not underutilize production capacity, which is 480 hours. (2) Achieve product demand of 40 (100-yard) lots for shag and 50 (100-yard) lots for sculptured carpet. Meeting demand for shag is more important than meeting demand for sculptured, by a ratio of 5 to 2. (3) Limit production overtime to 20 hours. a. Formulate a goal programming model to determine the amount of shag and sculptured carpet to produce to best meet the company’s goals. b. Solve this model by using the computer.
A semiconductor manufacturer produces a particular solid-state module that it supplies to four different television manufacturers. The module can be produced at each of the corporation's three plants, although the costs vary because of differing production efficiencies at the plants. Specifically, it costs 110 units to produce a module at plant A, 95 units at plant B and 103 units at plant C. Monthly production capacities of the plants are 7500, 10000, and 8100 modules, respectively. Sales forecasts project monthly demand at 4200, 8300,6300 and 2700 modules for television manufacturers I, II, III and IV respectively. If the cost for shipping a module from a factory to a manufacturer is as shown below, find a production schedule that will meet all needs at minimum total cost. II II IV 1 13 9. 19 В 1 16 1 14 2 13 1 15 4

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