A food company produces two types of emergency food,type t and type c,the food company received a contract. Let the variables t and c represent the amount of type t and type c. Goal 1:type t emergency food takes 10 hours to produce and type c takes 5 hours. The total number of work hoursavailable per period is approximately 3200 hours. Goal 2: one ton of type t uses 1 ton of flour and one ton of type c uses 0.5 ton of flour; 300 tons of flour are available for a period and no more can be bought. Goal 3: the company is committed to providing the aid agency with approximately 200 tons of type t emergency food in a period Goal 4: the demand for type c emergency food in the market is approximately 250 tons. question:(a) define deviation variable (b)objective function: to minimize sum of percentage deviation (c) state all constraints using deviation variables

A food company produces two types of emergency food,type t and type c,the food company received a contract. Let the variables t and c represent the amount of type t and type c. Goal 1:type t emergency food takes 10 hours to produce and type c takes 5 hours. The total number of work hoursavailable per period is approximately 3200 hours. Goal 2: one ton of type t uses 1 ton of flour and one ton of type c uses 0.5 ton of flour; 300 tons of flour are available for a period and no more can be bought. Goal 3: the company is committed to providing the aid agency with approximately 200 tons of type t emergency food in a period Goal 4: the demand for type c emergency food in the market is approximately 250 tons. question:(a) define deviation variable (b)objective function: to minimize sum of percentage deviation (c) state all constraints using deviation variables

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 74P: In this version of dice blackjack, you toss a single die repeatedly and add up the sum of your dice...

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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.
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.
You now have 5000. You will toss a fair coin four times. Before each toss you can bet any amount of your money (including none) on the outcome of the toss. If heads comes up, you win the amount you bet. If tails comes up, you lose the amount you bet. Your goal is to reach 15,000. It turns out that you can maximize your chance of reaching 15,000 by betting either the money you have on hand or 15,000 minus the money you have on hand, whichever is smaller. Use simulation to estimate the probability that you will reach your goal with this betting strategy.
The game of Chuck-a-Luck is played as follows: You pick a number between 1 and 6 and toss three dice. If your number does not appear, you lose 1. If your number appears x times, you win x. On the average, use simulation to find the average amount of money you will win or lose on each play of the game.
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?
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.
A company is operating in two unrelated businesses. The first one is making common salt, which is sold in one kilogram consumer packs. The second business is making readymade garments. The owner of the businesses has decided to implement Materials Requirement Planning (MRP) in one of the two businesses, which is likely to give him greater benefit. Assuming that the current turnover and profits of both the units are comparable, compare the relative benefits and limitations of Materials Requirement Planning (MRP) for these two businesses.
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.
It is known that there is a possibility that a group of people who are already working decide to continue working hours (overtime) is 30%. Because this group of people who continue working hours has a good commitment to the production target results of the company, then the possibility of that group of people getting sick is only 10%. Meanwhile, it is known that only 10% of these people get sick, while it is known that a group of people who do not continue working hours have a 20% chance of getting sick. There is a 60% chance for a group of sick people to be stressed, while the probability for a group of people who are not sick to be stressed is only 10%. In addition, a group of sick people also had the possibility to frequently permit work by 65%, while a group of people who were not sick also had the possibility to get permission to work only 45%. It is also known that a worker named Arief likes to eat a lot. Calculate the probability that Arief is a worker who likes to continue…
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 Woodruff Corporation purchased a piece of equipment three years ago for $211,000. It has an asset depreciation range (ADR) midpoint of eight years. The old equipment can be sold for $89,000. A new piece of equipment can be purchased for $321,500. It also has an ADR of eight years. Assume the old and new equipment would provide the following operating gains (or losses) over the next six years. Old equ 26,250 14,750 9,500 6,000 5,500 -6,500 The firm has a 25 percent tax rate and a 9 New equipment 81,000 74,500 70,750 61,250 51,500 46,750 year 1 4 percent cost of capital. What is the net cost of the new equipment? Round your solution to two decimal places. What is the present value of incremental benefits? Round your solution to two decimal places. What is the NPV of this replacement decision? Round your solution to two decimal places.
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%?