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 + 3x3 $ 160 minutes + 10x2 + 4x3 $ 288 hours + 2x2 + 4x3 $ 200 pounds X25 16 units X1. X2 X32 0 a-1. Are any constraints binding? Yes O No a-2. If so, which one(s)? Machine and materials Machine and labor O Materials Labor O None b-1. If the profit on product 3 changed to $22 a unit, would the decision variables' values change? Yes O No b-2. What would the new value of the objective function be? The objective function value = c-1. If the profit on product 1 changed to $22 a unit would the decision variables' values change? Yes c-2. Will the objective function value change, based on the change in C-1? c-2. Will the objective function value change, based on the change in c-1? Yes O NO 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 nction value change, based on the change in d-1? Yes O 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 f-2. What would be the new value of the objective function? The objective function value Z