A) The objective equation represents the net profit. In this case, the net profit can be calculated by multiplying the number of graphing calculators (x) by the profit per graphing calculator ($5), and subtracting the number of scientific calculators (y) multiplied by the loss per scientific calculator ($2).
Objective equation: Net Profit = 5x - 2y
B) The constraint equations can be derived from the given information:
1. Demand Constraint:
The demand for scientific calculators each day is at least 100, and the demand for graphing calculators is at least 80.
Scientific Calculator Constraint: y ≥ 100
Graphing Calculator Constraint: x ≥ 80
2. Production Capacity Constraint:
The production capacity for scientific calculators is a maximum of 200, and for graphing calculators is a maximum of 170.
Scientific Calculator Constraint: y ≤ 200
Graphing Calculator Constraint: x ≤ 170
3. Shipping Contract Constraint:
A total of at least 200 calculators must be shipped each day.
Total Calculator Constraint: x + y ≥ 200
C) To graph the associated constraint equations, we can plot them on a Cartesian plane.
D) To determine the vertices of each of the graphed equations, we need to find the points where the different constraints intersect. These intersection points are the vertices.
E) To determine the optimal number of each type of calculator to maximize net profits, we need to find the vertex that results in the highest net profit value.
We will find the solution in the following steps.