Sales & Operations Planning - LP A local firm manufactures children's toys. The projected demand over the next four months for one particular model of toy robot is given in the following table. Month Workdays Demand January February 23 3800 16 7200 March 20 2800 April 22 4400 Assume that a normal day is eight hours. Hiring costs are $350 per worker and firing costs are $850 per worker. Holding costs are $4 per unit held per month. Additionally, assume that it requires an average of two hours for one worker to assemble one toy. Shortages are not permitted. It is given that the ending inventory for December was 900 of these toys and the manager wishes to have at least 800 units on hand at the end of April. Assume that the current workforce level is 35 workers. The firm wants to minimize its cost. Answer the following questions. 1. Formulate the problem as a linear program. For simplicity, use the number from the questions instead of introducing parameter notations. Clearly define your variables and provide the objective function and constraints. 2. By looking at the numbers, could the producer avoid hiring new workers?

Sales & Operations Planning - LP A local firm manufactures children's toys. The projected demand over the next four months for one particular model of toy robot is given in the following table. Month Workdays Demand January February 23 3800 16 7200 March 20 2800 April 22 4400 Assume that a normal day is eight hours. Hiring costs are $350 per worker and firing costs are $850 per worker. Holding costs are $4 per unit held per month. Additionally, assume that it requires an average of two hours for one worker to assemble one toy. Shortages are not permitted. It is given that the ending inventory for December was 900 of these toys and the manager wishes to have at least 800 units on hand at the end of April. Assume that the current workforce level is 35 workers. The firm wants to minimize its cost. Answer the following questions. 1. Formulate the problem as a linear program. For simplicity, use the number from the questions instead of introducing parameter notations. Clearly define your variables and provide the objective function and constraints. 2. By looking at the numbers, could the producer avoid hiring new workers?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter3: Introduction To Optimization Modeling

Section3.8: A Multiperiod Production Model

Problem 18P: The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each...

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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?
If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
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
Nice-Fit is a (fictional) small business producing outfits for costume parties and specialoccasions. Custom designs can be tailored to a customer’s request. Tom and Ann are theowners of the company and source all the fabric, design the outfits and make the costumesthemselves. Tom and Ann keep spreadsheets with information on the material purchased andcostumes made, but they find it difficult to keep track of their products, raw materials, andsales. The raw materials are supplied from a fabric company in India, and the production takesplace in a manufacturing company in China. The clothing is sold at local weekend markets,sold, or rented through costume hire shops, and sold at their physical store. Tom and Annreceive a small percentage of the sales and rentals of their costumes from the hire shops.They have no information on customers other than those who request custom designsdirectly from them. In 2020, the Covid-19 pandemic had a major impact on global economies,businesses and how we…
Grey Manufacturing Company expects sales to total 13,000 units in the first quarter, 12,000 units inthe second quarter, and 15,000 units in the third quarter of the current fiscal year. Company policyis to have on hand at the end of each quarter an amount of inventory equal to 10% of the followingquarter’s sales. Given this information, how many units should be scheduled for production in thesecond quarter?
A. Write a document with the following information: 1. What do you expect your job to pay when you start? 2. What benefits are musts for you? 3. What benefits would you like to have even though they are not musts? 4. Include the graph you generate in step B below. B. Create a spreadsheet and a graph of life vs funds For each year of your remaining life specify the amount you plan to save/invest/withdraw that year and how much you expect that amount to increase during the year (base on actual data – typical savings interest rate, typical stock market interest rate, typical CDs, typical…). Calculate how much your funds will increase/decrease over your life and create a life (x-axis) vs funds (y-axis) plot.
The Feed ’N Ship Ranch fattens cattle for localfarmers and ships them to meat markets in KansasCity and Omaha. The owners of the ranch seek todetermine the amounts of cattle feed to buy so thatminimum nutritional standards are satisfied and atthe same time total feed costs are minimized. Thefeed mix can be made up of the three grains thatcontain the following ingredients per pound of feed: The cost per pound of stocks X, Y, and Z is $2, $4,and $2.50, respectively. The minimum requirementper cow per month is 4 pounds of ingredient A, 5pounds of ingredient B, 1 pound of ingredient C, and8 pounds of ingredient D.The ranch faces one additional restriction: itcan obtain only 500 pounds of stock Z per month from the feed supplier, regardless of its need. Be-cause there are usually 100 cows at the Feed ’N Ship Ranch at any given time, this means that no morethan 5 pounds of stock Z can be counted on for usein the feed of each cow per month.(a) Formulate this as an LP problem.(b) Solve using…
This type of operational planning may cover the medium‐term needs of the business including budgeting, the purchasing and supply system and organisation thereof, purchasing and supply methods, negotiation and development of human resources. (1) Strategic level planning. (2) Tactical or middle‐management planning. (3) Operations level planning. (4) Operational planning. (5) Short‐term planning. This is in fact a production or operations scheduling system and not an inventory control system. It eliminates the holding of inventory and is based on requiring suppliers to deliver materials of the right quality to the business on the day they are needed and where they are needed. (1) Cyclical‐ordering system. (2) Materials‐requirements planning. (3) Just in time. (4) System of fixed‐order quantities. (5) Quick response system.
A retired couple supplement their income by making fruit pies, which they sell to a local grocery store. During the month of September, they produce apple and grape pies. The apple pies are sold for $10.00 to the grocer, and the grape pies are sold for $8.00. The couple is able to sell all of the pies they produce owing to their high quality. They use fresh ingredients. Flour and sugar are purchased once each month. For the month of September, they have 1,500 cups of sugar and 2,400 cups of flour. Each apple pie requires 1½ cups of sugar and 3 cups of flour, and each grape pie requires 2 cups of sugar and 3 cups of flour. a. Determine the number of grape and the number of apple pies that will maximize revenues if the couple working together can make an apple pie in 6 minutes and a grape pie in 3 minutes. They plan to work no more than 60 hours. (Round your answers to nearest whole number.) b. Determine the amounts of sugar, flour, and time that will be unused. (Leave no cells blank -…
Although the company estimated that they will end with 400 units, the actual inventory on hand at the end of June was 350 units. The company doesn’t want to maintain a minimum target inventory. Due to challenges with recruiting process, they want to minimize labor and capacity costs. The rate to maintain inventory at end of each period per month is a holding cost of $1.5 per unit, and the company would like to have 600 units on hand at the end of December. Each unit requires five employee hours to produce, there are 22 working days each month and each employee works eight hours per day. Each employee produces 35.2 units per month. The work force at the end of June was 35 employees. On average, each employee is paid $2,800 per month. Based on the effort of interviewing and training new employees, the company estimates that it costs $2,000 for each employee hired. Firing pays amounts to $2,000 per employee. Determine a level production plan that minimizes arbitrary hiring and firing…
Information on a business is given below.Variable Expenses:Raw material expense: 250 TL / pieceAuxiliary equipment expense: 150 TL / pieceElectricity expenses: 100 TL / pieceSpare parts expense: 75 TL / pieceOther variable expenses: 125 TL / pieceFixed costs:Depreciation, interest and insurance expenses: 75 000 TLLabor and personnel expenses: 250 000 TLOther fixed expenses: 115 000 TLProduction capacity: 2000 pcs / monthSale price: 1600 TL / pieceAccording to the above,a) Find the break-even point as the production quantity?b) Find the amount that the business has to produce in order to make a profit of 500 000 TL / month?