TABLE 4.3 Demands for Owens-Wheat Problem Type 1 Type 2 200 Month 1 Month 2 Month 3 Month 4 300 200 300 100 400 200 Type 3 400 300 200 100 300 a. Determine how to minimize the total cost incurred during the next 4 quarters b. Use Solver Table to determine how much the total cost increases as the required capacity at the end of quarter 4 increases (from its current value of 4000) 11 Carco uses robots to manufacture cars. The following demands for cars must be met (not necessarily on time, but all demands must be met by end of quarter 4): 600 in quarter 1: 800 in quarter 2: 500 in quarter 3: 400 in quarter 4 At the beginning of the year, Carco has 2 robots Robots can be purchased at the beginning of each quarter, but a maximum of 2 per quarter can be purchased Each robot can build up to 200 cars per quarter It costs $5000 to purchase a robot Each quarter a robot incurs $500 in maintenance costs (even if it is not used to build any cats) Robots can also be sold at the beginning of each quarter for $3000 At the end of each quarter, a holding cost of $200 per car left in inventory is incurred If any demand is backlogged, a cost of $300 per car is incurred for each quarter the shortage lasts At the end of quarter 4, Carco must have at least 2 robots Determine how to minimize the total cost incurred in meeting demand for the next 4 quarters Owens-Wheat uses 2 production lines to produce 3 types of fiberglass mat. The demand requirements in tons) for each of the next 4 months are shown in Table 4.3 If it were dedicated entirely to the production of one product, a line 1 machine could produce either 20 tons of type I mat or 30 tons of type 2 mat during a month Similarly, a line 2 machine could produce either 25 tons of type 2 mat or 28 tons of type 3 mat It costs $5000 per month to operate a machine on line 1 and $5500 per month to operate a machine on line 2 A cost of S2000 is incurred each time a new machine is purchased, and a cost of $1000 is incurred if a machine is retired from service At the end of each month, Owens would like to have at least 50 tons of each product in inventory At the beginning of month 1, Owens has 5 machines on line 1 and 8 machines on line 2 Assume the per-ton cost of holding either product in inventory for one month is $5 a Determine a minimum cost production schedule for the next 4 months b. There is an important aspect of this situation that cannot be modeled by linear programming What is it? (Hint: If Owens makes product I and product 2 on line 1 during a month, is this as efficient as making just product 1 on line 1?) TABLE 4.3 Demands for Owens-Wheat Problem Type 1 Type 2 200 Month 1 Month 2 Month 3 Month 4 300 200 300 100 400 200 Type 3 400 300 200 100 300 a. Determine how to minimize the total cost incurred during the next 4 quarters b. Use Solver Table to determine how much the total cost increases as the required capacity at the end of quarter 4 increases (from its current value of 4000) 11 Carco uses robots to manufacture cars. The following demands for cars must be met (not necessarily on time, but all demands must be met by end of quarter 4): 600 in quarter 1: 800 in quarter 2: 500 in quarter 3: 400 in quarter 4 At the beginning of the year, Carco has 2 robots Robots can be purchased at the beginning of each quarter, but a maximum of 2 per quarter can be purchased Each robot can build up to 200 cars per quarter It costs $5000 to purchase a robot Each quarter a robot incurs $500 in maintenance costs (even if it is not used to build any cats) Robots can also be sold at the beginning of each quarter for $3000 At the end of each quarter, a holding cost of $200 per car left in inventory is incurred If any demand is backlogged, a cost of $300 per car is incurred for each quarter the shortage lasts At the end of quarter 4, Carco must have at least 2 robots Determine how to minimize the total cost incurred in meeting demand for the next 4 quarters Owens-Wheat uses 2 production lines to produce 3 types of fiberglass mat. The demand requirements in tons) for each of the next 4 months are shown in Table 4.3 If it were dedicated entirely to the production of one product, a line 1 machine could produce either 20 tons of type I mat or 30 tons of type 2 mat during a month Similarly, a line 2 machine could produce either 25 tons of type 2 mat or 28 tons of type 3 mat It costs $5000 per month to operate a machine on line 1 and $5500 per month to operate a machine on line 2 A cost of S2000 is incurred each time a new machine is purchased, and a cost of $1000 is incurred if a machine is retired from service At the end of each month, Owens would like to have at least 50 tons of each product in inventory At the beginning of month 1, Owens has 5 machines on line 1 and 8 machines on line 2 Assume the per-ton cost of holding either product in inventory for one month is $5 a Determine a minimum cost production schedule for the next 4 months b. There is an important aspect of this situation that cannot be modeled by linear programming What is it? (Hint: If Owens makes product I and product 2 on line 1 during a month, is this as efficient as making just product 1 on line 1?)