1. Three resources, R1, R2 and R3 will be used in producing two products, A and B. Each unit of A requires 4, 9 and 6 units of resources R1, R2 and R3 respectively, each unit of B requires 9 and 4 units of R1 and R2. The total number of units of products A and B should not be less than 140. At least 15 but not more than 45 units of A should be produced. Total amounts of the three resources available are 900, 700 and 1050 units. The profits for each unit of A and B are 5 and 7.

Formulate this as an LP problem to determine the number of units of each product to produce so as to maximize total profit.

Obtain the standard form for the following linear programming formulation.

Min 5P + 8Q + 4R

s.t. -3P + 4Q 55

8P + 5R 300

2P + 7Q + R 28

3Q - 6R 450

P, Q, R 0