Chapter 4.2, Problem 31E

Profit The Ball Company manufactures three types of lamps, labeled A, B, and C. Each lamp is processed in two departments, I and II. Total available work-hours per day for departments I and II are 400 and 600, respectively. No additional labor is available. Time requirements and profit per unit for each lamp type are as follows:

The company has assigned you as the accounting member of its profit planning committee to determine the numbers of types of A, B, and C lamps that it should produce in order to maximize its total profit from the sale of lamps. The following questions relate to a linear programming model that your group has developed. (For each part, choose one of the four answers.)

1. (a) The coefficients of the objective function would be
   1. (1) 4, 2, 3.
   2. (2) 2, 3, 1.
   3. (3) 5, 4, 3.
   4. (4) 400, 600.
2. (b) The constraints in the model would be
   1. (1) 2, 3, 1.
   2. (2) 5, 4, 3.
   3. (3) 4, 2, 3.
   4. (4) 400, 600.
3. (c) The constraint imposed by the available work-hours in department I could be expressed as
   1. (1) 4X₁ + 2X₂ + 3X₃ ≤ 400.
   2. (2) 4X₁ + 2X₂ + 3X₃ ≥ 400.
   3. (3) 2X₁ + 3X₂ + 1X₃ ≤ 400.
   4. (4) 2X₁ + 3X₂ + 1X₃ ≥ 400.