Antoni Manufacturing, a medium-size company, has been producing and selling three product families. Each product family requires production hours in each of four departments. In addition, each product family requires its own sales force, which must be supported no matter how large or small the sales volume happens to be. The parameters describing the situation are summarised in the following tables.

	Product Family
	P1	P2	P3
Profit per unit	$12.10	$12.70	$13.10

	Hours Required per 1000 Units			Hours Available
	P1	P2	P3
Department A	3	4	8	3,500
Department B	3	5	6	3,500
Department C	2	3	9	3,500
Department D	4	2	4	3,500
Sales cost	$60,000	$150,000	$70,000

a. Formulate the algebraic model by writing decision variables, objective function, and constraints. Note that your model should allow for the possibility that at least one of the product family is dropped.

b. Add a constraint to ensure that, if product family 1 (P1) is dropped, then product family 3 (P3) is not dropped.