Linear programming: Example: Suppose a factory want to produce two types of hand calculators, type A and type B. The cost, the labor time and the profit for every calculator is summarized in the following table: Type Cost Labor Time Profit A B $30 $20 1 (hour) 4 (hour) $10 $8 Suppose the available money and labors are $18000 and 1600 hours. What should the production schedule be to ensure maximum profit? [solution:] Suppose x1 is the number of type A hand calculators and x2 is the number of type B hand calculators. Then, we want to maximize p 10x1 8x2 subject to 30 x 20 y 18000 x 4 y 1600 x 0, y 0 where p is the total profit. The above equation and inequality can be transformed into the following linear system by employing some “dummy” variables, 10 x 8 y p 0 30 x 20 y u 18000 x 4y v 1600 x 0, y 0, p 0, u 0, v 0 1