A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of $5/unit of Product A and a profit of $2/unit of Product B. To manufacture a unit of Product A requires 6 min on Machine I and 5 min on Machine II. To manufacture a unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of machine time available on Machine I and 3 hr of machine time available on Machine II in each work shift. How many units of each product should be produced in each shift to maximize the company's profit? (x,y)= What is the optimal profit? (Round your answer to the nearest whole number.)

A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of $5/unit of Product A and a profit of $2/unit of Product B. To manufacture a unit of Product A requires 6 min on Machine I and 5 min on Machine II. To manufacture a unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of machine time available on Machine I and 3 hr of machine time available on Machine II in each work shift. How many units of each product should be produced in each shift to maximize the company's profit? (x,y)= What is the optimal profit? (Round your answer to the nearest whole number.)

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter10: Introduction To Simulation Modeling

Section: Chapter Questions

Problem 41P: At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 =...

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At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is 100, 90, 50, or 10, respectively. After observing the condition of the machine at the beginning of the week, the company has the option, for a cost of 200, of instantaneously replacing the machine with an excellent machine. The quality of the machine deteriorates over time, as shown in the file P10 41.xlsx. Four maintenance policies are under consideration: Policy 1: Never replace a machine. Policy 2: Immediately replace a bad machine. Policy 3: Immediately replace a bad or average machine. Policy 4: Immediately replace a bad, average, or good machine. Simulate each of these policies for 50 weeks (using at least 250 iterations each) to determine the policy that maximizes expected weekly profit. Assume that the machine at the beginning of week 1 is excellent.
In this version of dice blackjack, you toss a single die repeatedly and add up the sum of your dice tosses. Your goal is to come as close as possible to a total of 7 without going over. You may stop at any time. If your total is 8 or more, you lose. If your total is 7 or less, the house then tosses the die repeatedly. The house stops as soon as its total is 4 or more. If the house totals 8 or more, you win. Otherwise, the higher total wins. If there is a tie, the house wins. Consider the following strategies: Keep tossing until your total is 3 or more. Keep tossing until your total is 4 or more. Keep tossing until your total is 5 or more. Keep tossing until your total is 6 or more. Keep tossing until your total is 7 or more. For example, suppose you keep tossing until your total is 4 or more. Here are some examples of how the game might go: You toss a 2 and then a 3 and stop for total of 5. The house tosses a 3 and then a 2. You lose because a tie goes to the house. You toss a 3 and then a 6. You lose. You toss a 6 and stop. The house tosses a 3 and then a 2. You win. You toss a 3 and then a 4 for total of 7. The house tosses a 3 and then a 5. You win. Note that only 4 tosses need to be generated for the house, but more tosses might need to be generated for you, depending on your strategy. Develop a simulation and run it for at least 1000 iterations for each of the strategies listed previously. For each strategy, what are the two values so that you are 95% sure that your probability of winning is between these two values? Which of the five strategies appears to be best?
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.
A company makes two products (A and B). Each product requires time on two machines 1 and 2. the specifications for each product are as follows Product A Product B Processing time on machine 1 (hrs/unit) Processing time on machine 2 (hrs/unit) Material and labor cost (Sh./ unit) Selling price (Sh./ unit) Maximum possible sale (units) 2 1 2 14 15 16 18 130 150 The amount of time available on machine 1 is 360 hrs and on machine 2 is 260 hrs. Using simplex method determine the number of product A and B, which should be sold in order to maximize total contribution for the company.
Three methods can be used for producing heat sensors for high-temperature furnaces. Method A will have a fixed cost of $140,000 per year and a production cost of $62 per part. Method B will have a fixed cost of $210,000 per year and a production cost of $28 per part. Method C will require the purchase of equipment costing $500,000. It will have a life of five years and a 25% of first cost salvage value. The production cost will be $53 per part. At an interest rate of 10% per year, determine the breakeven annual production rate between the two lowest cost methods.
KAPC, a pharmaceutical company located in rural Kansas, is finding it difficult to retain its employees, who frequently leave after just six months of working at KAPC for jobs at pharmaceutical companies paying higher wages in Chicago. To address its problem with labor turnover, human resource officers at KAPC decide to run an experiment. Of their next 100 newly hired employees, 25 will randomly be selected to receive a housing voucher worth up to $4,000 per year to offset property taxes. To take advantage of this program, the employee must not only be randomly selected into the program but she must also purchase a home. Of the 25 employees selected into the housing voucher program, 7 leave KAPC within 12 months of starting. Of the 75 employees not selected into the program, 37 leave KAPC within 12 months of starting.a. Provide a difference-in-differences estimate of the effect the housing voucher program has on retention at KAPC.b. Suppose KAPC spends $10,000 in hiring costs each time…
The annual maintenance costs of a machine that has been in use for 3 years are 300 TL, 350 TL and 375 TL, respectively. The machine is expected to be available for 8 years after purchase. The maintenance costs foreseen for the coming years are 400 TL in the first year and 150 TL in the following years. If the machine is sold today, it can be sold for 1500 TL, and in the following years for 1000 TL. What is the optimum regeneration time of the machine if the MCVO is 10%?
A retail store sold in the month of April 5,000 products that produced $45,000 in sales. In the month of May the company sold 6,000 products. The store workforce consists of four full-time workers who work 40-hour week. In April the store also had seven part-time workers at 10 hours per week, and in May the store had nine part-timers at 15 hours per week (assume four weeks in each month). Using sales dollars as the measure of output (assume the price of the product was the same for both months), what is the percentage change in labor productivity from April to May? Answer: 2.
A scientist works in a lab with four summer interns and, as it is the end of the summer, he anticipates the head of the lab will ask him which of them he wants to retain. In terms of quality, the scientist and the head of the lab agree that intern A is better than intern B who is better than intern C who is better than intern D. The scientist would like to keep as many interns as possible and, given any number, the highest-quality ones. However, due to funding restrictions, the head of the lab wants to limit the number of interns that are retained. The head of the lab initially tells the scientist to select two interns to retain. After the scientist chooses two interns, the head of the lab decides whether to allow the scientist to retain a third intern. Thus, the sequence of moves is: 1) the scientist chooses two interns (both of whom are then retained); 2) the head of the lab decides either to allow the scientist to choose a third or not; and possibly 3) if the head of the lab chose…
The drum has a weight of 72 lb and a radius of gyration kO=0.4ft . If the cable, which is wrapped around the drum, is subjected to a vertical force P = 12 lb, determine the time needed to increase the drum's angular velocity from \omega 1=5rad/s to \omega 2=25rad/s . Neglect the mass of the cable.
Find the formula for g in terms of f. g(x) = -12 12 2.0 12 2.0 2.0 12 12 2.0 -12 Find the formula for g in terms of f. g(x) = -12
A large building may require an automated alarm system which monitors and controls all fire and security alarms in the building. Normally, the building is divided into zones and a number of alarms are associated with each zone. Alarms alert a central manned control area who may pass these on to the emergency services or may respond personally.Factors which have to be taken into account in building such a system are:Ø If the control area is unmanned and an alarm is activated this alarm should not be ignored if it is potentially serious. Emergency services should be automatically called.Ø Some but not all parts of the building may be equipped with sprinkler systems or systems to shut down electrical equipment. These should be activated if a fire alarm is confirmed. They should not be activated if there are people in the same room.Ø The building may be equipped with direction indicators which illuminate the route to the nearest exit. These should be activated when a fire alarm is…