HW1 Solution
Problem 1
Plot all of the constraints
Set constraint 1 as equality: 10A + 20B = 200
Set A = 0 → B = 10, 1st point (0,10)
Set B = 0 → A = 20, 2nd point (20,0)
Set constraint 2 as equality: 8A + 5B = 80
Set A= 0 → B = 16, 1st point (0,16)
Set B = 0 → A = 10, 2nd point (10,0)
Constraint 3 is a vertical line at A = 2
Constraint 4 is a horizontal line at B = 5
Iso-profit method: plot the O.F. by setting the O.F. equal to 300
60A + 50B = 300
A = 0 → B = 6, 1st point (0,6)
B = 0 → A = 5, 2nd point: (5,0)
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Y
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The optimal solution is point Y
Y is an intersection of constraint 1 and 2
10A + 20B = 200
8A + 5B =80
Multiplying (2) by 4 and subtract (1)
22A = 120 → A = 60/11
8(60/11) + 5B = 80 → B = 80/11
Y: (60/11,80/11)
The profit is 60(60/11) + 50(80/11) = 690.9
Problem 2
All of the constraints are the same. Therefore, the feasible solution area will be the same.
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Y
Z
W
