Given this linear programming model, solve the model and then answer the questions that follow. Maximize Subject to 12x1 + 18x2+ 15x3 where x1 = the quantity of product 1 to make etc. Machine Labor Materials Product 2 5x1 4x1 2x1 + 4x2 + 10x2 + 2x2 + 3x3 $ 160 minutes + 4x3 $ 288 hours + 4x3 $200 pounds X25 16 units X1 X2 X3 0 c-1. If the profit on product 1 changed to $22 a unit would the decision variables' values change? O Yes c-2. Will the objective function value change, based on the change in c-1? O Yes 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 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 $4 $16 O $72 1.1. If profit per unit on each product increased by $1, would the optimal values of the decision variables change? es O Yes No 1-2. What would be the new value of the objective function? The objective function value =