A company produces pants and shirts. Each pants requires three square yards of cloth, and each shirts requires two square yards of cloth. During the next two months the following demands for pants and shirts must be met (on time): month 1, 900 pants and 1300 shirts; month 2, 1200 pants and 1400 shirts. During each month the following resources are available: month 1, 9000 square yards of cloth; month 2, 6000 square yards of cloth. In addition, cloth that is available during month 1 and is not used can be used during month 2. During each month it costs $10 to produce an article of clothing with regular-time labor and $16 with overtime labor. During each month a total of at most 2400 articles of clothing can be produced with regular-time labor, and an unlimited number of articles of clothing can be produced with overtime labor. At the end of month 1, a holding cost of $1 per article is incurred for any article that will be carried over to be used in month 2. (There is no holding cost for cloth.) According to the specifications in the problem, what is the maximum number of shirts that can be produced in month 1? How many of the decision variables are zero at optimality? Not including non-negativities, how many constraints are necessary to solve this problem as a linear program?
A company produces pants and shirts. Each pants requires three square yards of cloth, and each shirts requires two square yards of cloth. During the next two months the following demands for pants and shirts must be met (on time): month 1, 900 pants and 1300 shirts; month 2, 1200 pants and 1400 shirts. During each month the following resources are available: month 1, 9000 square yards of cloth; month 2, 6000 square yards of cloth. In addition, cloth that is available during month 1 and is not used can be used during month 2. During each month it costs $10 to produce an article of clothing with regular-time labor and $16 with overtime labor. During each month a total of at most 2400 articles of clothing can be produced with regular-time labor, and an unlimited number of articles of clothing can be produced with overtime labor. At the end of month 1, a holding cost of $1 per article is incurred for any article that will be carried over to be used in month 2. (There is no holding cost for cloth.)
According to the specifications in the problem, what is the maximum number of shirts that can be produced in month 1?
How many of the decision variables are zero at optimality?
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