7.1) Billy Idell is trying to determine how many units of two types of lawn mowers 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 35 minutes of assembly time. The Standard model requires 10 minutes of inspection time, while the Deluxe model requires 15 minutes of inspection time. The company must fill an order for 6 Deluxe models. There are 450 minutes of assembly time and 180 minutes of inspection time available each day. How many units of each product should be manufactured to maximize profits?

7.2) Chewys produces a low-calorie dog food for overweight dogs. This product is made from beef products and grain. Each pound of beef costs $0.90, and each pound of grain costs $0.60. A pound of the dog food must contain at least 9 units of Vitamin 1 and 10 units of Vitamin 2. A pound of beef contains 10 units of Vitamin 1 and 12 units of Vitamin 2. A pound of grain contains 6 units of Vitamin 1 and 9 units of Vitamin 2. Formulate this as an LP problem to minimize the cost of the dog food. How many pounds of beef and grain should be included in each pound of dog food? What is the cost and vitamin content of the final product?