A pet food factory blends four ingredients into three types of pet food: value, premium, and basic. The maximum quantities available of each ingredient and the costs per ounce are given in the table below:

Ingredient	Maximum pounds available per day	Cost per ounce
1	5,000	$0.5625
2	2,400	$0.4375
3	4,000	$0.7500
4	1,500	$0.3750

The operations manager has placed limits on the component to be added to each blend. The limits and the selling price for each blend are shown in the table below:

Variant	Component Specifications	Selling Price per pound
Value	Not less than 40% of 1	$12.00
Value	Not more than 20% of 2	$12.00
Value	Not less than 30% of 3	$12.00
Premium	Not less than 40% of 3	$18.00
Basic	Not more than 50% of 2	$10.00
Basic	Not less than 10% of 1	$10.00

The marketing manager wants to produce at least 3,000 pounds of each variant of pet food.

1.1 Develop a linear programming model to help the company determine the best mix to produce to maximize profits.

1.2 Determine the optimal solution and recommend a strategy for producing pet food.