Question 2

(34 marks) A burger store sells two types of burgers: chicken burger and beef burger. Assume that the input for the two types of burgers can be viewed in terms of just four resources: bread, cheese, meat and labor.

The production of the two types of burgers in terms of these inputs is shown in the table below, along with the unit selling prices of the burgers.

	Chicken Burger	Beef Burger	Resources Available
Bread (pieces)	2	2	400
Cheese (slices)	2	1.5	300
Chicken (lbs)	0.5	/	50
Beef (lbs)	/	0.4	40
Cooking (hours)	0.3	0.4	70
Selling price	$33	$36.5	/

Bread can be obtained at $2 per piece, cheese can be obtained at $3 per slice, chicken can be obtained at $20 per lbs and beef costs $30 per lbs. The cooking time costs $10 per hour. Each resource is available in limited quantities as shown in the above table.

Assume the demand always exceeds the production capacities. The store owner would like to know how to decide on the production plan that maximizes the profit. Answer the following questions:

a. (4 marks) Write down the linear program to determine the optimal production plan.