Consider a company produces three different types of products (represented by a, b, and c as the production amounts in tons). The company would like to maximize its total output in tons and minimize its total cost in dollars that are expressed as follows: o Maximize a + b+ c o Minimize 200a + 300b + 400c Suppose we have a target tonnage of 10 tons and a target cost of 0 dollars. If you were to write a goal programming model for the company: a) Write the goal constraint for each of the above goals (Hint: To start, consider the targets as equality goal constraints. Use indexes "1" and "2" for the above goal constraints, respectively). b) What deviation variable would you use to minimize for the tonnage maximization goal? For the cost minimization goal? c) Write the objective function of the goal programming model for this problem using a weighted-sum approach, assuming that the tonnage goal is three times as important. Consider a company produces three different types of products (represented by a, b, and c as the production amounts in tons). The company would like to maximize its total output in tons and minimize its total cost in dollars that are expressed as follows: o Maximize a + b+ c o Minimize 200a + 300b + 400c Suppose we have a target tonnage of 10 tons and a target cost of 0 dollars. If you were to write a goal programming model for the company: a) Write the goal constraint for each of the above goals (Hint: To start, consider the targets as equality goal constraints. Use indexes "1" and "2" for the above goal constraints, respectively). b) What deviation variable would you use to minimize for the tonnage maximization goal? For the cost minimization goal? c) Write the objective function of the goal programming model for this problem using a weighted-sum approach, assuming that the tonnage goal is three times as important