Find the optimum number of batches (to the nearest whole number) of an item that should be produced annually (in order to minimize cost) if 270,000 units are to be made, it costs $4 to store a unit for one year, and it costs $340 to set up the factory to produce each batch 42 batches 40 batches 30 batches 28 batches

Find the optimum number of batches (to the nearest whole number) of an item that should be produced annually (in order to minimize cost) if 270,000 units are to be made, it costs $4 to store a unit for one year, and it costs $340 to set up the factory to produce each batch 42 batches 40 batches 30 batches 28 batches

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 40P

See similar textbooks

Similar questions

In Example 11.3, suppose you want to run five simulations, where the probability of passing inspection is varied from 0.6 to 1.0 in increments of 0.1. Use the RISKSIMTABLE function appropriately to do this. Comment on the effect of this parameter on the key outputs. In particular, does the probability of passing inspection have a large effect on when production should start? (Note: When this probability is low, it might be necessary to produce more than 25 batches, the maximum built into the model. Check whether this maximum should be increased.)
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Can you guess the results of a sensitivity analysis on the initial inventory in the Pigskin model? See if your guess is correct by using SolverTable and allowing the initial inventory to vary from 0 to 10,000 in increments of 1000. Keep track of the values in the decision variable cells and the objective cell.
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. As indicated by the algebraic formulation of the Pigskin model, there is no real need to calculate inventory on hand after production and constrain it to be greater than or equal to demand. An alternative is to calculate ending inventory directly and constrain it to be nonnegative. Modify the current spreadsheet model to do this. (Delete rows 16 and 17, and calculate ending inventory appropriately. Then add an explicit non-negativity constraint on ending inventory.)
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Modify the Pigskin model so that there are eight months in the planning horizon. You can make up reasonable values for any extra required data. Dont forget to modify range names. Then modify the model again so that there are only four months in the planning horizon. Do either of these modifications change the optima] production quantity in month 1?
In the lawn mower production problem in Example 8.4, experiment with the penalty cost for unsatisfied pickups in week 1. If this cost is sufficiently small, does the company ever produce fewer than seven models in week 1 and allow some week 1 pickups to be unsatisfied?
3-2) The optimal quantity of the three products and resulting revenue for Taco Loco is: A) 28 beef, 80 cheese, and 39.27 beans for $147.27. B) 10.22 beef, 5.33 cheese, and 28.73 beans for $147.27. C) 1.45 Z, 8.36 Y, and 0 Z for $129.09. D) 14 Z, 13 Y, and 17 X for $9.81. 3-3) Taco Loco is unsure whether the amount of beef that their computer thinks is in inventory is correct. What is the range in values for beef inventory that would not affect the optimal product mix? A) 26 to 38.22 pounds B) 27.55 to 28.45 pounds C) 17.78 to 30 pounds D) 12.22 to 28 pounds
A company produces three different products; x,y, and z. For the production of 1 unit of product x, 1 unit of A and 1 unit of B are used as input. 1 unit of A and 2 units of B are used to produce 1 unit of product y. To produce 1 unit of product z, only 1 unit of A is used. The company holds 40 units of A and 20 units of B periodically in total. By the way, the company can not produce product y more than the twice of product z. On the other hand, the sale price of 1 unit of product x is 10 TL, product y is 15 TL and product z is 12 TL. Furthermore, the cost of 1 unit of product x is 8 TL, product y is 9 TL and product z is 7 TL. According to above information, what should be the company’s optimal product mix to maximize its profit? Construct the problem as a Linear programming model. Solve the above problem by using Simplex Method.
Suppose 100,000 lamps are to be manufactured annually. It costs $1 to store a lamp for 1 year, $500 to set up the factory to produce a batch of lamps and $5 to produce each lamp. A. If all lamps are produced in one batch find the total cost? B. If all lamps are produced in two batches of equal size, find the total cost? C. If the number of units in each batch is q, then how many batches are there? D. Find the number of lamps in each batch to minmize the total cost? E. What is the minimum cost? [ i need all answer i will upvote]
you are thinking of opening a small copy shop. It costs $5000 to rent a copier for a year, and it cost $0.03 per copy to operate the copier. Other fixed costs of running the store withh amount to $400 per month. You plan to charge $0.10 per copy, and the store will be open 365 days per year. Each copier can make up to 100,000 copies per year. a. for one to five copiers rented and daily demands of 500, 1000, 1500, 2000 copies perday, find annual profit. That is, find annual profit for each of these combinations of copiers rented and daily demand. b. if you rent three copies, what daily demand for copies will allow you to break even? c. Graph profit as a function of the number of copiers for a daily demand of 500 copiers; for a daily demand of 2000 copies. Interpret your graph
The company is interested in determining when to produce a batch of speakers , and how many speakers to produce to each batch. b. Suppose now that the unit cost for every speaker is $11 if less than 10,000 speakers are produced, $10 if production falls between 10,000 and 80,000 speakers, and $9.50 if production exceeds 80,000 speakers. What is the optimal policy?
(Need both parts a and b) During the next four months, a customer requires, respectively, 500, 650, 1000, and 700 units of a commodity, and no backlogging is allowed (that is, the customer’s requirements must be met on time). Production costs are $50, $80, $40, and $70 per unit during these months. The storage cost from one month to the next is $20 per unit (assessed on ending inventory). It is estimated that each unit on hand at the end of month 4 can be sold for $60. Assume there is no beginning inventory. A. What is the objective function in this problem? B. What are the constraints in this problem? Write algebraic expressions for each
each Distributors packages and distributes industrial supplies. A standard shipment can be packaged in a class A container, a class K container, or a class T container. A single class A container yields a profit of $10; a class K container, a profit of $8; and a class T container, a profit of $12. Each shipment prepared requires a certain amount of packing material and a certain amount of time. Formulate and solve this problem using LP software. Resources Needed per Standard Shipment Class of Container Packing Material (pounds) Packing Time (hours) A 2 2 K 1 6 T 3 4 Total amount of resource available per week 120 pounds 210 hours Hugh Leach, head of the firm, must decide the optimal number of each class of container to pack each week. He is bound by the previously mentioned resource restrictions but also decides that he must keep his 6 full-time packers employed all 210 hours (6 workers × 35 hours)…