Problem 19-15 (Static) Given this linear programming model, solve the model and then answer the questions that follow. 12X1 + 18X2+ 15x3 where x1 = the quantity of product 1 to make etc. Maximize Subject to Machine Labor Materials Product 2 5X1 4X1 2X1 + 4x2 10x2 + 2x2 S + 3x3 5 160 minutes + 4X3 288 hours +4x3 $ 200 pounds X2 16 units X1 X2 X3 2 a-1. Are any constraints binding? Yes ONo a-2. If so, which one(s)? Machine and materials Machine and labor Materials O Labor O None b-1. If the profit on product 3 changed to $22 a unit, would the decision variables' values change? O Yes No b-2. What would the new value of the objective function be? b-2. What would the new value of the objective function be? The objective function value Z = c-1. If the profit on product 1 changed to $22 a unit, would the decision variables' values change? O Yes ONo c-2. Will the objective function value change, based on the change in C-1? O Yes d-1. If 10 hours less of labor time were available, would the decision variables values change? Yes O NO d-2. Will the objective function value change, based on the change in C-1? Yes No e. If the manager decided that as many as 20 units of product 2 could be produced (instead of 16), how much additional profit would be generated? $0 $4 $16 $72 f-1. If profit per unit on each product increased by $1, would the optimal values of the decision variables change? Yes NO f-2. What would be the new value of the objective function? The objective function value Z =