Question

CNY Furniture manufactures two kind of coffee tables. The first one is a larger table, called Adirondack. Each Adirondack has six table legs and a table top of 18 square feet. The second one is a smaller table, called Bismarck. Each Bismarck has four table legs and a table top of 16 square feet. In order to plan for its monthly production, the management has 420 table legs and 1440 square feet of table top material available for each month.

Due to the recent demand from a local new apartment project, at least 10 Bismarck tables must be manufactured monthly. Furthermore, the limited storage space restricts the monthly production of the larger Adirondack to be no more than 60 Adirondack tables.

Each Adirondack can bring in a net profit of $300 which each Bismarck can bring in $250. CNY Furniture needs to plan for its monthly production that can maximizes its total monthly profit.

1) Formulate this problem as a linear program.

Answer 1

To formulate this problem as a linear program, we need to define the decision variables, constraints, and objective function. The objective is to maximize the total monthly profit, subject to constraints on table legs, table top material, minimum Bismarck tables, and maximum Adirondack tables.

Step-by-step explanation:

To formulate this problem as a linear program, we need to define the decision variables, constraints, and objective function.

Let:

• x = number of Adirondack tables to produce
• y = number of Bismarck tables to produce

The objective is to maximize the total monthly profit, so the objective function is:

Maximize Z = 300x + 250y

Subject to the following constraints:

• 6x + 4y ≤ 420 (table legs constraint)
• 18x + 16y ≤ 1440 (table top material constraint)
• y ≥ 10 (minimum Bismarck tables constraint)
• x ≤ 60 (maximum Adirondack tables constraint)

Additionally, x and y must be non-negative.