Question

(a) Problem Statement

Montana wood products manufacture two high quality products, tables and chairs. Its profit is $15 per chair and $21 per table. Weekly production is constrained by available labor and wood. Each chair requires 4 labor hours and 8 board feet of wood, while each table requires 3 labor hours and 12 board feet of wood. Available wood is 2400 board feet and available labor is 920 hours. Management also requires at least 40 tables and at least 4 chairs to be produce d for every table. To maximize profits, how many chairs and tables should be produced?

(b) Decision Variables

Let C denote number of chairs and let T denote the number of tables

(c) Objective Function

Our goal is to Maximize profit. The Objective Function is Max P = 15C1 + 21T2

(d) Constraints

Each constraint represents a different limiting factor, and this problem has two: hours of labor and amount of wood.

Labor: 4C1 + 3T2 ≤ 920
Wood: 8C1 + 12T2 ≤ 2400

Also, since we can't produce a negitive number of table and chairs, we must imclude the non-negativity constraints:

C1, T2 ≥ 0 and Integer

(e) Mathematical Statement of the Problem

Max P = 15C1 + 21T2

S.T.
4C1 + 3T2 ≤ 920
8C1 + 12T2 ≤ 2400
T2 ≥ 40
C1 - 4T2 ≥ 0
C1, T2 ≥ 0 and Integer

(f) Optimal Solution - You present the optimal solution. It is not enough to state the solution. You must provide support for your answer. You may use Excel or the graphical solution method.

Answer 1

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