A firm manufactures pills in two sizes A and B. A contains 2 grains of aspirin, 5 grains of bicarbonate and 1 grains of codeine. B contains 1 grain of aspirin, 8 grains of bicarbonate and 6 grains of aspirin, 74 grains of bicarbonate and 24 grains of codeine for providing immediate effect. It is required to determine the least number of pills a patient should take to get immediate relief. Formulate the problem as a standard LPP and solve it graphically.
To formulate the problem as a standard Linear Programming Problem (LPP), you can follow these steps:
Step 1: Define the decision variables:
Let's denote the number of pills of size A to be produced as 'x' and the number of pills of size B to be produced as 'y'.
Step 2: Formulate the objective function:
The objective is to minimize the number of pills a patient should take to get immediate relief. In this case, the objective function is the total number of pills, which can be expressed as:
Z = x + y
Step 3: Formulate the
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A businessman needs 5 cabinets, 12 desks and 18 shelves cleaned out. He has two part time employees, Rashid and Ruby. Ruby can clean 1 cabinet, 3 desks and 3 shelves in a day while Rashid can clean 1 cabinet, 2 desks and 6 shelves in one day. Rashid is paid Rs.22 per day and Ruby is paid Rs.25 per day. In order to minimize the cleaning costs, for how many days should Rashid and Ruby be employed? Formulate the problem as a linear programming problem and find its solution by simplex method.
Prove that the dual of dual of a LPP is primal LPP.
Test for convexity the following sets:
S = {(x, y) | x2 + y2 >1, y > x, y > - x}
S = {(x, y) | x2 + y2 <16, x < 2, y > 2}
Solve the (4X3) game with pay off matrix.
At each stage, clearly explain the steps involved.
Solve the following game by graphical method.
For the transportation problem given below. Check whether the given basic feasible solution is optimal. If not, modify the given solution and find an optimal solution and the optimal value for the problem.
| 6 | 1 (25) | 9 | 3 (45) | 70 |
| 11 | 5 (5) | 2 (50) | 8 | 55 |
| 10 (85) | 12 (5) | 4 | 7 | 90 |
| 85 | 35 | 50 | 45 |
For the following matrix game, write down the equivalent LPPs for solving the game.
B