A
manufacturing company produces two products, A and B, at two different plants,
1 and 2. Plant 1 has resources
available to produce 500 units of either product (or a combination of products)
daily, and plant 2 has enough resources to produce 800 units. The cost for each product at each plant is
as follows.

Product
A 
Product
B 
Plant 1 Plant 2 
$50 60 
$45 30 
Plant 1 has
a daily budget of $20,000, and plant 2 has a budget of $30,000. Based on past sales, the company knows it
cannot sell more than 600 units of product A and 800 units of product B. The selling price for product A is $80 and
for product B is $70. The company
wishes to know the number of units of A and B to produce at plants 1 and 2 to
maximize profits.
Formulate a linear programming model for this problem.