Resource allocation podunk institute of technology’s math deaprtment offers two cources: finite math and applied calculus.each section of finite math has 60 studnets, and each section of applied calculus has 50. The department is allowed to offer a total of up to 110 sections. Furthermore, no more than 6000 studnets want to take a math course( no student will take more than one math course) draw the feasible region that shows the number of sections of each class that can be offered. Find the corner points of the region.

To find the feasible region, which represents the combinations of sections of each class that can be offered, we need to consider the following constraints:

1. Each section of finite math has 60 students, and each section of applied calculus has 50 students.
2. The department can offer up to 110 sections in total.
3. The total number of students cannot exceed 6000.

Let's assign the variables:
x = Number of sections of finite math (each section has 60 students)
y = Number of sections of applied calculus (each section has 50 students)

Based on the given information, we can establish the following constraints:

Constraint 1: x + y ≤ 110
This represents the constraint that the department can offer a total of up to 110 sections.

Constraint 2: 60x + 50y ≤ 6000
This represents the constraint that the total number of students taking math courses cannot exceed 6000.

Now, let's graph these constraints:

Step 1: Plot the x and y axes.

Step 2: For the first constraint, x + y ≤ 110, plot the line x + y = 110. To do this, find two points that satisfy the equation (for example, (0, 110) and (110, 0)), and draw a line passing through them.

Step 3: For the second constraint, 60x + 50y ≤ 6000, we need to convert it to slope-intercept form (y = mx + b). Divide the entire equation by 10 to simplify it: 6x + 5y ≤ 600. Rewrite it as y ≤ -6/5x + 120. Plot this line by finding two points that satisfy the equation, and draw a line passing through these points.

Step 4: Shade the feasible region. The feasible region is the area of the graph that satisfies both constraints. Shade the region below the lines in the graph.

Step 5: Find the corner points of the feasible region. These points are where the shading intersects, which represent the optimal solutions.

By analyzing the graph, you can find the corner points of the feasible region and determine the combinations of sections of each class that can be offered based on the given constraints.