d) An additional 12 hours of time available for the second machine, at no cost to the firm, are going to increase the objective value byresponse to two decimal places).dollars (round your Maximize contribution =4x₁ + 4x2 +7x31X₁ +7X2 +4X3 ≤ 802X1 + 1X2 +7X3 ≤ 848X1 + 4X2 + 1X3 ≤ 80X1, X2, X3 ≥0(C₁: hours on machine 1)(C2: hours on machine 2)(C3: hours on machine 3)a) Using a computer software for solving LP, the optimal solution achieved is:✗₁= 6.25 (round your response to two decimal places).X25.11 (round your response to two decimal places).X3 9.48 (round your response to two decimal places).Contribution (objective value) = 111.86 (round your response to two decimal places).b) Machine 1 has 0 hours of unused time available at the optimal solution (round your response to two decimal places).Machine 2 has 0 hours of unused time available at the optimal solution (round your response to two decimal places).Machine 3 has 0 hours of unused time available at the optimal solution (round your response to two decimal places).c) An additional hour of time available for third machine, is worth 0.26 dollars to the firm (round your response to two decimal places).

EXplanation is as followsIncrease involvement84 8X1 + 4X2+1X3 ≤ 80 X1, X2, X3 20 X + 4X2 + X3 1X1…

Answered: d) An additional 12 hours of time…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.3: The Exponential Distribution

Problem 3P

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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?
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.
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.

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