תכנון ייצור חברה הפסיקה את קו ייצורו של אחד ממוצריה הלא רווחיים. בעקבות כך נוצרה אפשרות לייצור נוסף של התוצרים האחרים (עודף ייצור). לפיכך ההנהלה רוצה לנצל את עודף ייצור זה לאחד או יותר משלושת מוצריה הנוספים. את יכולת הייצור של המכונות ניתן לראות בטבלה הבאה: AVAILABLE TIME MACHINE TYPE (HOURS PER WEEK) Milling Machine 200 Lathe 100 Grinder 50 כמו כן את מספר השעות הדרושות לייצור יחידת מוצר עבור כל אחד משלושת המוצרים ניתן לראות בטבלה הבאה: MACHINETYPE PRODUCT I PRODUCT 2 PRODUCT 3 Milling Machine 8 2 3 Lathe 4 3 0 Grinder 2 0 1 מחלקת המכירות סבורה כי הפוטנציאל המכירה של מוצרים 1 ו2 עבור את הייצור המירבי ואילו פוטנציאל המכירה של מוצר 3 הינו 20 יחידות לשבוע. הרווח ליחידת מוצר הינו 8$,6$,20$: עבור מוצרים 3,2,1 בהתאמה. כמה מוצרים צריכה החברה לייצר מכל מוצר על מנת למקסם את רווחיה?

PRODUCTION PLANNING A manufacturing firm has discontinued production of a certain unprofitable product line. This has created considerable excess production capability. Management is considering devoting this excess capability to one or more of three products. The available capacity on the machines is summarized in the following table: AVAILABLE TIME MACHINE TYPE (HOURS PER WEEK) Milling Machine 200 Lathe 100 Grinder 50 The number of machine hours required for each unit of the respective products is: PRODUCTIVITY ( HOURS PER WEEK) MACHINETYPE PRODUCT I PRODUCT 2 PRODUCT 3 Milling Machine 8 2 3 Lathe 4 3 0 Grinder 2 0 1 The sales department indicates that the sales potential for products 1and 2 exceeds the maximum production rate and that sales potential for product 3 is 20 units per week. The unit profit would be $20, $6, and $8, respectively on products 1, 2, and 3. How much of each product should the firm produce in order to maximize profit?

MARKET SURVEY ( שווק סקר) Market Survey, Inc. (MSI), is a marketing firm that specializes in evaluating consumer research to new products, services, and advertising campaigns. A client firm has requested assistance from MSI in ascertaining consumer reaction to a recently marketing product for household use. During meetings with the client it was agreed that door-to-door personal interviews would be used to obtain information from both households with children and households without children. In addition, it was agreed that both day and evening interviews would be necessary in order to allow for a variety of household work schedules. Specifically, the clients contract called for MSI to conduct 1000 interviews with the following quota guidelines: At least 400 households with children would be interviewed. At least 400 households without children would be interviewed. The total number of households interviewed during the evening would be at least as great as the number of households interviewed during the day. At least 40% of the interviews for households with children would be conducted during the evening. At least 60% of the interviews for households without children would be conducted during the evening. Since the interviews of households with children take additional interviewer time, and since evening interviewers are paid more than daytime interviewers, the cost of an interview varies with the type of interview. Based on previous research studies, estimates of the interview costs are as follows: INTERVIEW COST HOUSEHOLD DAY EVENING Children $20 $25 No children $18 $20 What is the household, time-of-day interview plan that will satisfy the contract requirements at a minimum total interviewing cost?

LABOR PLANNING ( עבודה מתכננת) McCarthy’s Everyday Glass Company is planning to produce two styles of drinking glasses during the next month. The glasses are processed in four separate departments. Excess equipment capacity is available and will not be a constraining factor. However, the company’s labor resources are limited and will probably limit the production volume for the two products. The labor requirements per case of one dozen glasses produced is: HOURS OF LABOR PER CASE OF PRODUCT DEPARTMENT PRODUCT I PRODUCT 2 1 0.070 0.100 2 0.050 0.084 3 0.100 0.067 4 0.010 0.025 The company makes a profit of $1.00 per case of product I and $0.90 per case of product 2. Because of the training and experience qualifications of the workers, the production manager has some flexibility in allocating labor resources across the 4 departments as shown in the table below: POSSIBLE LABOR ASSIGNMENTS HOURS OF LABOR AVAILABLE DEPARTMENT I ONLY 430 DEPARTMENT 2 ONLY 400 DEPARTMENT 3 ONLY 500 DEPARTMENT 4 ONLY 135 DEPARTMENTS I OR 2 570 DEPARTMENTS 3 OR 4 300 TOTAL AVAILABLE 2335 What is the product mix and labor allocation that will maximize profit?

FINANCIAL-MIX STRATEGY ( אסטרטגית ערבוב כספית) The Jefferson Adding Machine Company will begin production of two new models of electronic calculators during the next three months. Since these models require an expansion of the current production operation, the company will need operating funds to cover material, labor, and other expenses during the initial production period. Revenue from this initial production period will not be available until after the end of the period. Thus, the company must arrange financing for these operating expenses before production can begin. Jefferson has set aside $3,000 in internal funds to cover expenses of this operation. If additional funds are needed, they will have to be generated externally. A local bank has offered a line of short-term credit in an amount no to exceed $10,000. The interest rate over the life of the loan will be 12% per year on the average amount borrowed. One stipulation set by the bank requires that the remainder of the company cash set aside for this operation plus the accounts receivable for this product line be at least twice as great as the outstanding loan plus interest at the end of the initial production period. In addition to the financial restrictions placed on this operation, labor capacity is also a factor for Jefferson to consider. Only 2500 hours of assembly time and 150 hours of packaging and shipping time are available for the new product line during the initial 3-month production period. Relevant cost, price, and production time requirements for the two models, referred to as Y and Z, are shown below: LABOR HOURS REQUIRED SELLING PROFIT PACKAGING & MODEL UNIT COST PRICE MARGIN ASSEMBLY SHIPPING Y $50 $58 $8.12 12 1 Z $100 $120 $20.25 25 2 Additional restrictions have been imposed by company management in order to guarantee that the market reaction to both products can be tested; that is, at least 50 units of model Y and at least 25 units of model Z must be produced in the first production period. All units of each model are sold as they are produced to independent distributors and the average rate of turnover of accounts is three months. Develop an LP to determine how much production should be supported by the internally generated funds and how much by the externally generated funds in order to maximize Jefferson’s profit?

BLENDING ( לערבב) The Grand Strand Oil Company produces regular-grade and premium-grade gasoline products, which are sold to independent service stations in the southeastern United States. The Grand Strand refinery manufactures the gasoline products by blending three petroleum components. The gasoline products are sold at different prices, and the petroleum components have different costs. Data available show that the regular-grade gasoline can be sold for $0.50 per gallon and the premium-grade gasoline for $0.54 per gallon. For the current production planning period, Grand Strand can obtain the three petroleum components at the cost per gallon and in the quantities shown below: PETROLEUM COMPONENT COST PER GALLON MAXIMUM AVAILABLE COMPONENT 1 $0.25 5,000 GALLONS COMPONENT 2 $0.30 10,000 GALLONS COMPONENT 3 $0.42 10,000 GALLONS The product specifications for the regular and premium gasoline products restrict the amounts of each component that can be used in each gasoline product. The product specifications are: PRODUCT SPECIFICATIONS REGULAR GASOLINE AT MOST 30% COMPONENT 1 ATLEAST 40% COMPONENT 2 AT MOST 20% COMPONENT 3 PREIMUM GASOLINE AT LEAST 25% COMPONENT 1 AT MOST 40% COMPONENT 2 AT LEAST 30% COMPONENT 3 Current commitments to distributors require Grand Strand to produce at least 10,000 gallons of regular-grade gasoline. The firm would like to determine how to mix or blend the three components into the two gasoline products in such a way as to maximize profits.