Maxell manufacturing makes three models of pens: Ballpoint pen, fountain pen and
ID: 3175382 • Letter: M
Question
Maxell manufacturing makes three models of pens: Ballpoint pen, fountain pen and rollerball pen. One lot of ballpoint pen sells for $740, and uses $120 worth of raw materials and $35 worth of labor cost. One lot of fountain pen sells for $835, and uses $160 worth of raw materials and $41 worth of labor cost. One lot of rollerball pen sells for $975, and uses $210 worth of raw materials and $54 worth of labor cost. Requirement for each lot of pens are given below: Each month, Maxell has 32 lbs. of plastic, 51.25 fl. oz, of ink, and 44 labor hours. Demand for ballpoint and fountain pens are unlimited, but at most 12 lots of rollerball pens can be manufactured each month. Formulate a linear programming model that can be used to determine the number of lots of each model that should be produced in order to give Maxell highest possible monthly profit (Write the complete model for the problem. Make sure to give clear definitions of your decision variables). Solve the problem by using Excel Solver (Hand-in both the value and formulas printouts for the problem). Show the optimal solution and optimal value in your printouts.Explanation / Answer
Let x, y and z be the number of lots to be manufactured each month of Ballpoint, Fountain and Rollerball pens respectively.
Constraint 1: Plastic requirement
6/5x + 5/4y + z <= 32
24x + 25y + 20z <= 640
Constraint 2: Ink requirement
4/5x + y + 5/4z <= 51.25
16x + 20y + 25z <= 1025
Constraint 3: Labor
3/9x + 7/6y + 4/3z <= 44
6x + 21y + 24z <= 792
Constraint 4:
z <= 12
Profit = (740-120-35)x + (835-160-41)y + (975-210-54)z
Profit = 585x + 634y + 711z
Hence the problem can be formulated as,
Maximize Z = 585x + 634y + 711z
subject to,
24x + 25y + 20z <= 640
16x + 20y + 25z <= 1025
6x + 21y + 24z <= 792
z <= 12
Hence in order to maximize the profit, 0 lots of ballpoint, 16 lots of fountain and 12 lots of ballroller pens should be manufactured and the maximized profit would be $18676
Solver Solution x y z Total Demand Decision Variables 0 16 12 Profit 585 634 711 18676 Constraint 1 24 25 20 640 640 Constraint 2 16 20 25 620 1025 Constraint 3 6 21 24 624 792 Constraint 4 0 0 1 12 12