Billy Penny is trying to determine how many units of two types of lawnmowers to produce each day. One of these is the Standard model, while the other is the Deluxe model. The profit per unit on the Standard model is $60, while the profit per unit on the Deluxe model is $40. The Standard model requires 20 minutes of assembly time, while the Deluxe model requires 30 minutes of assembly time. The Standard model requires 10 minutes of inspection time, while the Deluxe model requires 15 minutes of the inspection time. The company must fill an order for 5 Deluxe models. There are 400 minutes of assembly time and 180 minutes of inspection time available each day.

a) Specify the linear program and identify all the constraints

b)How many units of each product should be manufactured to maximize profits?

c) What is the maximum profit can the company make?

d)Are any constraints redundant? If so, which one or ones?

Let X = number of Standard models to produce Y = number of Deluxe models to produce