State the linear programming problem in mathematical terms, identifying the obje

Question

State the linear programming problem in mathematical terms, identifying the objective function and the constraints. A firm makes products A and B. Product A takes 3 hours each on machine L and machine M; product B takes 3 hours on L and 2 hours on M. Machine L can be used for 11 hours and M for 6 hours. Profit on product A is S9 and $10 on B. Maximize profit. A. Maximize 9A + 1O B Subject to: 3A + 3BS11 2A + 3B greaterthanorequalto 11 B. Maximize 10A + 9B Subject to: 3A + 2B greaterthanorequalto 11 3A + 3B greaterthanorequalto 6 A, B greaterthanorequalto 0 C. Maximize 9A + 1 OB Subject to: 3A + 3B greaterthanorequalto 11 3A + 2B greaterthanorequalto 6 A, B greaterthanorequalto 0 D. Maximize 9A + 1O B Subject to: 3A + 3B lessthanorequalto 11 2A + 3B lessthanorequalto 6 A, B greaterthanorequalto 0

Explanation / Answer

Answer Option: C

Maximize 9A+10B Subject to:3A+3B<=11 3A+2B<=6

                    A,B>=0

Consider

product A

Product B.

Given that

a) Product A takes 3 hours each on machine L and machine M;

b) Product B takes 3 hours on L and 2 hours on M.

c) Machine L can be used for 11 hours and M for 6 hours

maximize profit?

The objective function for maximisation is a profit function: which is:
P (A, B) = 9A+10B

Applying the constraints:

With a given Maximum limit of11 hours, total hours that a machine L can be used

The constraint is :3A+3B<=11

With a given Maximum limit of 6 hours, total hours that a machine M can be used

The constraint is: 3A+2B<=6

And A, B>=0

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