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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 s.t. B C Department A 1.5p + 1.50 Department B 2.00 0.25 Product 2 X 3.00 x 1.00 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 $25 for product 1, $27 for product 2, and $29 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 25p1 +27p2+ 39p3 Your answer cannot be understood or graded. More Information Product 3 2.00 2.50 with profit s 0.25 Your answer cannot be understood or graded. More Information Department C P P P20 (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)? (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 $350 for product 1, $510 for product 2, and $620 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