ESI 6314
Homework #1 Solutions
Problem 1
x
1
=
Number of Type 1 Trucks produced daily
x
2
=
Number of Type 2 Trucks produced daily
Expressing profit in hundreds of dollars we obtain the following formulation:
max z =
3x
1
+ 5x
2
s.t.
x
1
/800 + x
2
/700
≤
1 (Paint Shop Const.)
x
1
/1500 + x
2
/1200
≤
1 (Engine Shop Const.)
x
1
≥
0, x
2
≥
0
AB is x
1
/800 + x
2
/700 = 1. CD is x
1
/1500 + x
2
/1200 = 1.
Feasible region is bounded by ABE. Dotted line is z = 3x
1
+ 5x
2
= 1500. Moving isoprofit line up
and to right we find optimal solution to be where x
1
≥
0 and Paint Shop constraint are binding.
Thus x
1
= 0, x
2
= 700, z = 3500(in hundreds) is optimal solution.
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Problem 2
5. True. If feasible region is bounded, moving parallel to isoprofit line will eventually cause us to
leave feasible region. Thus if feasible region is bounded, the LP cannot be unbounded.
6. False. Consider the Dorian auto example of Section 3.2.
Problem 3
8. The LP is infeasible, because no points can satisfy the last two constraints.
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 Fall '09
 VLADIMIRLBOGINSKI
 Optimization, Comparison of raster graphics editors, The LP, LP album, D. E. Marsh

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