Wildcat Coffee Inc., includes three different kinds of coffee beans (Arabica, Robusta, and Liberica) to blend its three coffee products (Burst, Dawn, and Smokey). The cost per pound, the availability, and rating information of the coffee beans are as follows.

Coffe Bean	Cost Per Pound	Caffeine Rating	Taste Ratting	Aroma Rating	Available Pounds
Arabica	$2.25	7	9	8	600
Robusta	$1.52	9	5	7	850
Liberica	$2.75	8	7	9	960

Coffee product tests provide ratings on a 1-10 scale, with higher ratings indicating higher product performance. Here are the three coffee products and their product information:

Coffee Product	Selling Price per Pound	Product Segment	Product Information
Burst	$4.95	High Caffeine	Caffeine level rates at least 8.1 or higher; Taste level rates at least 7.2 or higher; No Aroma level requirement
Dawn	$3.05	Low Price	No requirement on caffeine level; Tastes level rates no more than 7.3; Aroma level rates no more than 8.4.
Smokey	$5.75	Gourmet	No requirement on caffeine level; Taste level at least 8.5; Aroma level at least 8.6

Due to the popular demand of the low-price segment, at least 875 pounds of Dawn must be produced.

Set up and list the linear programming model for the above problem. (You do not need to solve the listed model).