18-1
CHAPTER 18 SOLUTIONS
18.1
The unknowns are A and B, the quantities of A and B produced in gal/week.
The objective function is:
A,B
(1) max
5A + 3.5B
J
=
The constraints are:
AB
(2) 2
6,000
[Type 1 columns are available 6,000 hrs/week]
100
100
i.e.
2A + B
600,000
(3)
4
10,000
[Type 2 columns are available 10,000 hrs/week]
100
100
i.e.
A + 4B
1,000,000
+
≤
≤
+
≤
≤
The graphical solution of the LP is shown above, were it is noted that the feasible
region is constrained by the quantities of the two types of columns that are
available [Eqs. (2) and (3)]. The three coordinates of the feasible region
boundaries are possible optimal solutions. Their examination gives:
1: A = 0 gal,
B = 250,000 gal
⇒
J = $875,00/week
2: A = 200,000 gal
B = 200,000 gal
⇒
J = $1,700,000/week
3: A = 300,000 gal
B = 0 gal
⇒
J = $1,500,000/week
Clearly, the optimal solution is to produce 200,000 gal each of A and B, for which the
profit is maximized, at $1,700,000/week.