FinFone Paper Mill is a small-scale paper-making company which produces four different types of paper. Each type of paper must go through processing on four different machines. The manufacturing time (in minutes) per unit of paper produced is listed in the following table.
?
Time required (in minutes)
PaperType
Machine Type
A
B
C
D
1
2.4
1.2
2.7
3.2
2
2.1
2.4
3.2
3.3
3
1.6
0.9
2.6
5.1
4
2.5
2.5
3.2
6.5
?
The maximum time allotted for each machine is 30 hours per week and at least 100 units of each type of paper should be made during the week.
?
Profit per unit is:
Paper Type
A
B
C
D
Profit ($)
0.25
0.32
0.44
0.5
?
Develop and solve an all-integer model that will determine, using the available machine time, the number of units of each paper type to be produced in order to meet the weekly demand and to maximize the profit.
What will be an ideal response?
B = Number of units of Type B paper made
C = Number of units of Type C paper made
D = Number of units of Type D paper made
Max 0.25A + 0.32B + 0.44C + 0.5D
s.t.
2.4A + 1.2B + 2.7C + 3.2D£ 1800
2.1A + 2.4B + 3.2C + 3.3D£ 1800
1.6A + 0.9B + 2.6C + 5.1D£ 1800
2.5A + 2.5B + 3.2C + 6.5D£ 1800
A, B, C, D³ 100
A, B, C, D³ 0 and integer
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