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: 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 $28 for product 1,$30 for product 2 , and $25 for product 3 . (a) Formulate a linear programming model for maximizing total profit contribution. If the constant is " 1" it must be entered in the box. If required, round your answers to two decimal places. Let Pi= units of product i produced 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? (b) Solva the figear progrsm formalated in part (a). How muen of esch groduct should be product, snd what is the projected total profit contribution? Profit 1 (c) After eveiuating the solution obtaines in part (b) one of the zrodvetion rupervisars nated that graduction satup costi pad nt been taken into aftount. She incted that satup covts wre stoo far product 1. 1550 far product 2, and 3400 for product 3 . If the solution developed in part (b) is to be used, ahat is the tutal pratt coedrbution after tak ing into account the setup casts? 1 (d) Management realized that the optimel prosuct mis, taing sutup cotes ines account, might bu dirfarane from the one recornmended in part (b). Formulate a mived-integer inese program that taias satup costa provided in part (c) into account. Management also stated that we should not cancider making mere than 175 inits ef praduct 1, 150 unile of product 2, ar 140 units of produtt J. Whot are the new objective functon and adtronal aquation conatraints? If the constont is " 1 " it must se enteres in the bec. Let Y is one if any quantity of product i it produced and zero of-hereite. If the constant is " 1 " it must be entered in the box. 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: 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 $28 for product 1,$30 for product 2 , and $25 for product 3 . (a) Formulate a linear programming model for maximizing total profit contribution. If the constant is " 1" it must be entered in the box. If required, round your answers to two decimal places. Let Pi= units of product i produced 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? (b) Solva the figear progrsm formalated in part (a). How muen of esch groduct should be product, snd what is the projected total profit contribution? Profit 1 (c) After eveiuating the solution obtaines in part (b) one of the zrodvetion rupervisars nated that graduction satup costi pad nt been taken into aftount. She incted that satup covts wre stoo far product 1. 1550 far product 2, and 3400 for product 3 . If the solution developed in part (b) is to be used, ahat is the tutal pratt coedrbution after tak ing into account the setup casts? 1 (d) Management realized that the optimel prosuct mis, taing sutup cotes ines account, might bu dirfarane from the one recornmended in part (b). Formulate a mived-integer inese program that taias satup costa provided in part (c) into account. Management also stated that we should not cancider making mere than 175 inits ef praduct 1, 150 unile of product 2, ar 140 units of produtt J. Whot are the new objective functon and adtronal aquation conatraints? If the constont is " 1 " it must se enteres in the bec. Let Y is one if any quantity of product i it produced and zero of-hereite. If the constant is " 1 " it must be entered in the box