A company manufactures two types of boxes, corrugated and ordinary cartons. The boxes undergo two major processes: cutting and pinning operations. The profits per unit are $6 and $4 respectively. Each corrugated box requires 2 minutes for cutting and each carton requires 3 minutes for cutting, whereas each corrugated box requires 2 minutes for pinning and each carton requires 1 minute for pinning. The available cutting time is 120 minutes and total pinning time is 60 minutes. Determine the optimum quantities of the two boxes to maximize the profits. a. Formulate a linear programming model that can be used to determine the quantities of the two boxes that should be produced in order to maximize total profit contribution b. Graph the feasible region. c. Determine the coordinates of each extreme point.
A company manufactures two types of boxes, corrugated and ordinary cartons. The boxes undergo
two major processes: cutting and pinning operations. The profits per unit are $6 and $4
respectively. Each corrugated box requires 2 minutes for cutting and each carton requires 3 minutes
for cutting, whereas each corrugated box requires 2 minutes for pinning and each carton requires
1 minute for pinning. The available cutting time is 120 minutes and total pinning time is 60
minutes. Determine the optimum quantities of the two boxes to maximize the profits.
a. Formulate a linear programming model that can be used to determine the quantities of the two
boxes that should be produced in order to maximize total profit contribution
b. Graph the feasible region.
c. Determine the coordinates of each extreme point.
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