Final answer:
The minimum value of the function C = x + 3y subject to a set of inequality constraints can be found by graphing the constraints and identifying the vertex of the feasible region that minimizes C, or by using linear programming techniques.
The correct answer is C = 11.33
Step-by-step explanation:
The student has asked to find the minimum value of C = x + 3y, given a set of constraints. To solve this optimization problem, we can use graphical methods or linear programming techniques. First, we should graph the inequality constraints on a coordinate plane:
- 9x + 2y > 35
- x + 3y > 14
- x > 0
- y > 0
The feasible region is the intersection of the half-planes defined by these inequalities. To find the minimum value of C, we look for the vertex (corner point) of the feasible region that provides the smallest value of C.
This usually occurs at the intersection of two constraint lines. In this case, we need to turn the inequalities into equalities (9x + 2y = 35 and x + 3y = 14) to find their intersection points with each other and with the axes (x = 0 and y = 0).
Once we plot these lines and find the feasible region, we can test the value of C at each vertex to identify the minimum value.
If we cannot plot these lines or find the intersection points, we may use linear programming methods such as the Simplex algorithm to find the optimal solution. Without additional information or context, we are unable to calculate the exact minimum value of C.
The correct answer is C = 11.33