9781118041581

The first inequality reflects the fact that the programs together must

increase oxygen by 6 mg/liter. The right-hand side lists this minimum require-

ment. The left-hand side shows the total amount of oxygen generated by the

programs. For instance, spending $2 million on each program (D F 2)

would increase oxygen by (3)(2)  2 8 mg/liter, which would more than

meet the goal. In turn, the left-hand side of the second constraint shows the

reduction in chlorine: 10 mg per million spent on the first program plus 20 mg

per million on the second. The nonnegativity constraints, D 0 and F 0,

complete the formulation.

Figure 17.3 shows the graph of the feasible region. The main point to

observe is the impact of the “greater than or equal to” constraints. The feasi-

ble region lies above the two-sided boundary AZB. (Make sure you understand

that the constraint lines are properly graphed. Check the intercepts!)

716 Chapter 17 Linear Programming

0 12345 6 7

Amount Spent on Program D

1

2

3

4

5

6

7

Amount Spent on Program F

Z

A

Oxygen constraint

Chloride constraint

B

FIGURE 17.3

Clean-Water Funding

At point Z, $1 million

is spent on program D

and $3 million on

program F. This plan

meets the oxygen and

chloride constraints at

minimum total cost.

c17LinearProgramming.qxd 9/26/11 11:05 AM Page 716