Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows.

Department	Product 1	Product 2	Product 3
A	1.50	3.00	2.00
B	2.00	1.00	2.50
C	0.25	0.25	0.25

During the next production period, the labor-hours available are 450 in department A, 350 in department B, and 50 in department C. The profit contributions per unit are $24 for product 1, $27 for product 2, and $28 for product 3.

(a) Formulate a linear programming model for maximizing total profit contribution. (Let P, - units of product i produced, for i = 1,2,3.) Max st. Department A Department B Department Pq. P, Pg 20 (b) solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contribution (in dollars)? P. P. Py) - with profits (c) After evaluating the solution obtained in part (b), one of the production supervisors noted that production setup costs had not been taken into account. She noted that setup costs are $360 for product 1, $500 for product 2, and 5650 for product 3. If the solution developed in part (b) is to be used, what is the total profit contribution (in dollars) after taking into account the setup costs? $ Management realed that the optimal productie taking up costs into account, might be different from the one recommended in part). Formate aminteger linear program that is setup Couns into HOMAM, Managanaana also stated that we should not consider making more than 100 units a prout i 175 units of product a * 105 ants a product a tions - anits of gration producers and In addition to the constraints from part(), what other countries should be added to the integer linear program units of Product produced its of Product produced ) - was wors