Formulate the algebraic model for this problem by writing down the decision variables, objective function, and constraints. Note that your model should allow for the possibility that one or more of the products are dropped.

A company produces three products. Each product has an annual demand potential, a unit margin, and an annual fixed cost. The fixed cost can be avoided if the product is not produced at all. This information is summarised in the following table.

Product	Demand	Unit margin	Fixed cost
1	290,000	$1.20	$60,000
2	200,000	$1.80	$200,000
3	50,000	$2.30	$55,000

Each product requires the following production hours on three machines.

	Hours Required per Thousand Units			Hours Available
Machine	Product 1	Product 2	Product 3
A	3	4	8	1,900
B	3	5	6	1,900
C	2	3	10	1,900

b. Add a constraint to ensure that the following requirement is met.

If product 2 is dropped, then product 3 is dropped.

• Formulate the algebraic model for this problem by writing down the decision variables, objective function, and constraints. Note that your model should allow for the possibility that one or more of the products are dropped.

A company produces three products. Each product requires its own sales force, which must be supported no matter how large or small the sales volume happens to be, unless the product line is eliminated. Product demands, unit margins, and sales force costs are summarised in the following table.

Product	Demand	Unit margin	Sales force cost
1	7,000	$52	$60,000
2	4,000	$35	$50,000
3	3,000	$45	$70,000

Each product also requires the following production hours in three departments.

	Hours Required per Thousand Units			Hours Available
Department	Product 1	Product 2	Product 3
A	3	4	7	2,000
B	3	4	6	2,000
C	2	3	8	2,000

• Add a constraint to ensure that the following requirement is met.

If product 1 is dropped, then product 3 is not dropped.