Linear Programming, & Statistical Quality Control Possible 1. Bill Penny is trying to determine how many units of two types of lawn mowers to produce each day. One of these is the standard model, X, while the other is the deluxe model, Y. The profit per unit on the standard model is $40, while the profit on the deluxe model is $50. The standard model requires 15 minutes of assembly time, while the deluxe model requires 45 minutes of assembly time. The standard model requires 10 minutes of inspection time, while the deluxe model requires 20 minutes of inspection time. The company must fill an order for at least 5 deluxe models. There are 450 minutes of assembly time and 180 minutes of inspection time available each day. a. Write out the \"objective function\" for this problem. b. How many units of each lawn mower should be manufactured to maximize profits? That is, what is the optimal output solution. c. What is the profit associated with the optimal solution? d. How much could the profit on X (standard model) increase or decrease without changing the optimal solution? e. Are any of the constraints \"binding?\" If so, identify those constraints that are binding