8.7: Linear Programming- A Geometric Approach

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Linear Inequalities in Two Variables

Maximization Applications

1) 80 acres of wheat and 20 acres of corn should be planted for a maximim profit of $8,400.
2) 10 chairs and 15 tables should be manufactured for a maximum profit of $650.
3) The maximum value of X is 40 when $x$ = 0 and $y$ = 4.

Minimization Applications

1) 30 units of Food A and 45 units of Food B should be purchased to keep costs at a minimum of $105.
3) min C = 12,000 $x$ + 10,000 $y$
    s.t. 200 $x$ + 100 $y$ $\ge$ 800 (high-grade oil)
         300 $x$ + 100 $y$ $\ge$ 900 (medium-grade oil)
         200 $x$ + 200 $y$ $\ge$ 1,000 (low-grade oil)
   Refinery A should be operated for 3 days while Refinery B should be operated for 2 days for a minimum cost of $56,000.

Chapter Review

1) (16000, 4000); $2,240
2) (2, 3); $34,000
3) (8, 20); $480
4) (12000, 8000)
5) (72, 180); $5,760
6) (165, 35); $21,750
7) (20, 60); $34
8) (20, 20); $2.40
9) (6, 18); $1,650
10) (35, 100); $2,600
11) (40, 20); $100,000
12) (10, 5); 17.5 minutes
13) (1000, 800); $7,400

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