This is liner programming problem for optimization of an objective function subject to some liner constraints. There are two profit maximization problems and two cost minimization problems.
For each problems below complete the following:
a) Graph and label every inequality. State the scale used on both axes.
b) Shade the feasible region.
c) State the coordinates of all corner points.
d) Evaluate the objective function for every corner point.
e) State the optimal value of the objective function along with the coordinates of the corner point. For the last two problems state the final answer in practical words.
1) Solve the following linear programming problems using the method of corners.
Maximize P = 3x + 2y subject to (see attached file for equations).
2) Solve the following linear programming problem using the method of corners.
Minimize C = 2x + 4y subject to (see attached file for equations)
3) K.L. Manufacturing wants to maximize its profit on products A and B. The profit on one unit of Product A is $40, while the profit on Product B is $20. Each unit of Product A requires 10 hours of assembly time and 2 hours of finishing time, while each unit of Product B requires 2 hours of assembly time and 4 hours of finishing time. The departmental capacity (in total hours) is 20,000 for assembly and 31,000 for finishing. What is the maximum profit, and how many of each product should be produced to achieve that profit? Write the objective function and system of linear inequalities and solve it graphically using the method of corners.
4) Two varieties of animal feed contain essential nutrients A and B. Feed I contains 2 units of A and 3 units of B per pound. Feed II contains 2 units of A and 5 units of B per pound. A farmer needs a feed mix that will give his animals a minimum of 16 units of A and 30 units of B. If Feed I costs $3 per pound and Feed II costs $4 per pound, how much of each should be bought to supply the proper nutrition while minimizing cost? Write the objective function and system of linear inequalities and solve it graphically using the method of corners.