Question

G&G Furniture Co. produces chairs and tables. The following table gives the profit generated per unit, as well as the amount of wood, labor and other materials required, per unit of each product along with their maximum monthly limits in terms of availability.

	Chairs	Tables	Max Limits
profit	$100	$125
Wood	20 lbs per unit	30 lbs per unit	6000 lbs
Other Materials	1 lbs per unit	1 lbs per unit	400 lbs
Labor	1.5 hours per unit	2 hours per unit	300 hours

In addition to the above, you are told that the number of Chairs produced must not be more than 100 units greater than the number of Tables produced. Lastly, you are told that any linear programming solution cannot give non-integer values for the number of Tables and Chairs to be produced.

2 Given that G&G Furniture Co. wants to earn the highest possible profits without violating these constraints, help the company decide how many tables and chairs to produce by answering the following questions:

a) Clearly list down the decision variables, the objective function and the constraints in words. You will be marked for the clarity of your definition of these parameters as well the use of the standard verbal (Step 1) format for these parameters outlined in your textbook (and in class).

b) Clearly provide the mathematical expressions, equations and inequalities for the objective function and the constraints in the summary (Step 2) format prescribed in your textbook (and in class).

c) Formulate the mathematical linear programming model for this problem using Microsoft Excel and use Microsoft Excel Solver Add-in to solve the problem. You will be marked for clarity of formatting and labelling and using the Excel setup correctly.

d) How many of each type of product do you recommend G&G Furniture Co. should produce per month to optimize their level of profit? e) What would be the profit at this level?

Answer 1

(c).

(d). 142 chairs and 43 tables should be produced

(e). Profit made = $19575