In the model X1, X2, and X3 are the number of units of three products or services to make. The constraints are: machine time (minutes), labor (hours), budget (in $), and a limit on the number of units of X3. The objective is to maximize profit. Note: assume that fractional results are allowed. Max profit = 22X1 + 20X2 + 10X3 s.t. Machine time: 8X1 + 3X2 + 4X3 <= 111 minutes Labor: 2X1 + 9X2 + 3X3 <= 300 hours Budget: 1X1 + 5X2 + 2X3 <= $190 Product 3: X3 <= 20 units a. What are the optimal solution and its profit? 6.66667, TP = 133.33 b. Which of the constraints are tight? Which are not tight? For those not tight, how much resource is left-over? P3 is tight. c. Give the range of values for the per unit profit on each product X1, X2, and X3 for which the current solution remains optimal. Please show your work.