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 + 1x2 + 2x2 33 160 minutes + 4X3 288 hours + 4X3 $200 pounds X25 16 units X1 X2 X3 2 a-1. Are any constraints binding? Yes a-2. If so, which one(s)? a-2. If so, which one(s)? Machine and materials O 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? Yes No 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 O No 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? O Yes O No d-2. Will the objective function value change, based on the change in d-1? d-2. Will the objective function 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? O $0 O $4 O $16 O $72 1-1. If profit per unit on each product increased by $1, would the optimal values of the decision variables change? Yes NA f-2. What would be the new value of the objective function? The objective function value =