Given this linear prohramming model, solve the model and then answer the question that follow Maximize Z= 12x1 + 18x2 + 15x3 Where xi = the quantity of product 'i' to make Subject to: Machine Labor Materials Product 2 5x1 + 4x2 + 3x3 4x110x2 + 4x3 2x1 + 2x2 + 4x3 X2 x1, x2,x3

Given this linear prohramming model, solve the model and then answer the question that follow Maximize Z=121+182+153 Where xi= the quantity of product ' i ' to make Subject to: MachineLaborMaterialsProduct251+42+3341+102+4321+22+4321,2,3160minutes288hours200pounds16units0 a. Are any constraints binding? If so, which one(s)? b. If the profit on product 3 were changed to $22a unit, what would the values of the decision variables be? The objective function? Explain c. If the profit on product 1 were changed to $22 a unit, what would be the vales of the decision variables be? The objective function? Explain d. If 10 hours less of labor time were available, what would be the vales of the decision variables be? The objective function? Explain 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? f. If profit per unit on each product increased by $1, would the optimal values of the decision variables change: Explain. What would the optimal value of the objective function be