Problem 3 (10 marks). Products 1, 2, and 3 require time for their production in each of four

departments. The weekly capacities of the four departments can be expressed in terms of the

number of units of each of the three products that each department could produce in a week, as

follows:

Department	Product1 CAP/Week		Product 2 CAP/Week		Product 3 CAP/Week
1	150	or	60	or	80
2	50	or	70	or	20
3	100	or	40	or	60
4	30	or	50	or	70

The data in the above table have the following meaning, using department 1 as an example: by virtue of its production capacity, department 1 can produce 150 units of product 1, or 60 units of product 2, or 80 units of product 3, or any linear combination of these. The profit for product 1 is $6/unit, for product 2 is $8/unit, and for product 3 is $5/unit. We wish to know how many units of each product to make, per week, if the profitability of the output is to be maximized, subject to the capacity constraints. You are asked to formulate a mathematical model (no solution is required) for the problem.