Example Y Example 2.3.4. Consider the operation of one division in a large plant. The division is responsible for manufacturing two parts of the plant's final product. The division manager has available four different processes to produce these two parts; each pro- cess uses various amounts of labor and two raw materials. The inputs and outputs for 1 hr of each of the four processes are given in the following table. Raw Material B Labor Process (worker-hours) 1 2 30 3 10 4 25 20 Input Raw Material A (lb) 160 100 200 75 30 Output Units of Units of Part 1 Part 2 35 55 42 70 0 0 90 35 45 60 80 The division is responsible for producing each week 2100 units of Part 1 and 1800 units of Part 2. The division manager has at her disposal each week 4 tons of Raw Material A and 2 tons of Raw Material B and 1000 hr of labor. One pound of Raw Material A costs the firm $3, and one pound of Raw Material B costs $7. Because of labor contracts, the plant must pay its employees a full week's salary, regardless of whether or not the employees are used that week, so the cost of the 1000 hr of labor is fixed. However, the division manager can request her workers to work up to an extra 200 hr per week in overtime at a cost of $30/hr to the firm. The plant vice- president in charge of production wants to know if the division can meet its weekly production requirements with the material on hand without using overtime and, if so, the minimal cost of this operation. And, because the decision to allow overtime must he made at the plant level, the vice-president also wants some estimate on how much money, if any, the division can save by using overtime. Example Y Example 2.3.4. Consider the operation of one division in a large plant. The division is responsible for manufacturing two parts of the plant's final product. The division manager has available four different processes to produce these two parts; each pro- cess uses various amounts of labor and two raw materials. The inputs and outputs for 1 hr of each of the four processes are given in the following table. Raw Material B Labor Process (worker-hours) 1 2 30 3 10 4 25 20 Input Raw Material A (lb) 160 100 200 75 30 Output Units of Units of Part 1 Part 2 35 55 42 70 0 0 90 35 45 60 80 The division is responsible for producing each week 2100 units of Part 1 and 1800 units of Part 2. The division manager has at her disposal each week 4 tons of Raw Material A and 2 tons of Raw Material B and 1000 hr of labor. One pound of Raw Material A costs the firm $3, and one pound of Raw Material B costs $7. Because of labor contracts, the plant must pay its employees a full week's salary, regardless of whether or not the employees are used that week, so the cost of the 1000 hr of labor is fixed. However, the division manager can request her workers to work up to an extra 200 hr per week in overtime at a cost of $30/hr to the firm. The plant vice- president in charge of production wants to know if the division can meet its weekly production requirements with the material on hand without using overtime and, if so, the minimal cost of this operation. And, because the decision to allow overtime must he made at the plant level, the vice-president also wants some estimate on how much money, if any, the division can save by using overtime
