Solve the problem:
Q: Suppose that a firm seeks to maximize revenue, R = 5x1 + 4x2, by choosing to produce quantities of two goods, x1 and x2, subject to certain linear production constraints. These production constraints represent respectively the constraints linked to labour, capital, and raw resources required to produce quantities x1 and x2:
2x1 + x2 = 13
3x1 + 5x2 = 30
4x1 + x2 = 24.
with x1 = 0, x2 = 0.
Represent this linear programming problem in matrix form, transforming in the process the inequality constraints into equality constraints by the addition of slack variables, s1, s2 and s3. Then, utilizing the values of your extreme points found in
a), Find the corresponding values of the slack variables in each case.
b) Finally, express these extreme points along with their respective values of the slack variables as vectors in a five-dimensional space (i.e. 5 × 1 vectors). How many non-zero elementsdo you find in each, and how do you explain this result?