Question

QDM Question 5 : A company is attempting to decide the mix of products which it should produce next week. It has six products, each with a unit profit (unit profit =selling price –variable cost per unit) and a unit production time as shown below:

Product	Profit ($/unit)	Production time (hours/unit)
1	10	1
2	22	2
3	35	1.7
4	19	2.4
5	55	4.5
6	115	9.5

The company has 720 hours available next week. The company has the following additional linear constraints:

• If any of the above six products are produced a fixed cost of $1000 is incurred.
• If product 3 is produced, 40 hours are needed for production setup.

Formulate an integer programming model to find next week production schedule at maximize profit with linear objective function and all linear constraints.

Decision variables (1 mark):

Objective function (1 mark):

Constraints :

Additional constraint 1 : Product 1 must be produced if any of Product 2, 3 and 4 is produced.

Additional constraint 2 : Product 3 must be produced if all of Product 4, 5 and 6 are produced.

Answer 1