(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. Eachchair requires 4 labor hours and 8 board feet of wood, while eachtable requires 3 labor hours and 12 board feet of wood. Availablewood is 2400 board feet and available labor is 920 hours.Management also requires at least 40 tables and at least 4 chairsto be produce d for every table. To maximize profits, how manychairs and tables should be produced?
(b) Decision Variables
Let C denote number of chairs and let T denote the number oftables
(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 thisproblem 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 andchairs, 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 isnot enough to state the solution. You must provide support for youranswer. You may use Excel or the graphical solution method.
