Manufacturingand marketing data for a production situation. there are 3 departments: punch, welding, assembly. there are also 3 products: a,b,c. product A passing punch department for 2 hours and in the assembly department for 5 hours. product B passing punch department for 3 hours and in welding department for 2.5 hours. product C passing punch department for 2 hours and in the welding department for 1.5 hours and in the assembly department for 2.5 hours. capacity of punch department is 1200 hours, capacity of welding department is 600 hours, and capacity of assembly department is 1500 hours. the objective is to determine the quantity of product A,B,and C to produce so that total profit will be maximized. the profit for product A is 0.6, product B is 0.7, and product C is 0.5

question: formulate the problem as a linier programming.