An individual wishes to invest $5000 over the next year in two types of investment: investment A yields 5% and investment B yields 8%. market research recommends an allocation of at least 25% in A and at most 50% in B. Moreover, investment in A should be at least half the investment in B. Formulate this as a linear programming problem.
Solve the following LP problem using Simplex method
Maximizez=3x1+2x2+x3Maximize \quad z = 3x_1 + 2x_2 + x_3Maximizez=3x1+2x2+x3 Subject tox1+x2+x3≤9Subject\ to \quad x_1 + x_2 + x_3 \le 9Subject tox1+x2+x3≤9 2x1+3x2+5x3≤302x_1 + 3x_2 + 5x_3 \le 302x1+3x2+5x3≤30 2x1−x2−x3≤82x_1 - x_2 - x_3 \le 82x1−x2−x3≤8 x1,x2,x3≥0x_1, x_2, x_3 \ge 0x1,x2,x3≥0
What is operations research? Why operations research is important in the field of Mechanical Engineering?
Alumco manufacturers Aluminum sheets and Aluminum bars. The maximum production capacity is estimated at either 800 sheets or 600 bars per day. The maximum daily demand is 550 sheets and 560 bars. The profit per ton is $40 per sheet and $35 per bar. Formulate the problem as a linear programming problem.
Use graphical method to solve the following problem
Maximizez=2x1+3x2Maximize \quad z = 2x_1 + 3x_2Maximizez=2x1+3x2
Subject tox1+x2≤1Subject \ to \quad x_1 + x_2 \le 1Subject tox1+x2≤1
3x1+x2≤43x_1 + x_2 \le 43x1+x2≤4
x1,x2≥0x_1, x_2 \ge 0x1,x2≥0
What is operation research? State any 2 models in operation research with at least one example.
A firm manufactures 2 types of products A and B and sells them at a profit of $2 on type A and $3 on type B. Each product is processed on 2 machines C and D. Type A requires 1 minute of processing time on C and 2 minutes on D. Type B requires 1 minute on C and 1 minute on D. The machine C is available for not more than 6 hours 40 minutes while machine D is available 12 hours during any working day. Formulate the problem as a linear programming problem.
Solve the following LP problem using graphical method Minimize z=2x1+3x2z = 2x_1 + 3x_2z=2x1+3x2 Subject to x1+x2≥6x_1 + x_2 \geq 6x1+x2≥6 7x1+x2≥147x_1 + x_2 \geq 147x1+x2≥14 x1,x2≥0x_1, x_2 \geq 0x1,x2≥0