A factory makes three different types of product: ordinary, premium, and deluxe. Each product is made using four different machines: A, B, C, and D.

Each ordinary product needs 5 minutes on machine A, 8 minutes on machine B, and 4 minutes on machine D. It costs $8 to make a ordinary product. Revenue of a ordinary product is $12.

Each premium product needs 7 minutes on machine A, 4 minutes on machine B, and 11 minutes on machine C, and 10 minutes on machine D. It costs $12 to make a premium product. Revenue of a premium product is $17.

Each deluxe product need 13 minutes on machine C and 9 minutes on machine D. It costs $18 to make a deluxe product. Revenue of a deluxe product is $25.

Machine A is available for 6 hours a day, machine B for 5 hours a day, machine C for 8 hours a day, and machine D for 4 hours per day. The budget is $1200 per day.

The factory must make:

At least 45% of total production must be premium product.

Number of deluxe products must be less than twice the total number of ordinary and premium products.

Formulate (without solving) a linear programming question to maximize the total profit while satisfying the constraints.