Final answer:
To find the minimum value of C = 10x + 26y subject to the given constraints, we use the method of linear programming to graph the feasible region, evaluate the objective function at each corner point, and find the minimum value of C.
Step-by-step explanation:
To find the minimum value of C = 10x + 26y subject to the constraints x+y≤6, 5x + y ≥ 10, and x + 5y ≥ 14, we can use the method of linear programming. We will graph the feasible region determined by the three inequalities and evaluate the objective function at each corner point to find the minimum value of C.
The feasible region is the region where all the inequalities are satisfied. By graphing the inequalities, we find that the feasible region is a polygon with vertices at (2,4), (2,6), (4,2), and (6,0).
Finally, we evaluate the objective function at each corner point:
- Point (2,4): C = 10(2) + 26(4) = 108
- Point (2,6): C = 10(2) + 26(6) = 172
- Point (4,2): C = 10(4) + 26(2) = 68
- Point (6,0): C = 10(6) + 26(0) = 60
Therefore, the minimum value of C is 60 when x = 6 and y = 0.