A. The order in which you define the variables isn't fixed. For the sake of this discussion, let's define them like this:
x = Number of bookshelves
y = Number of tables
B. Due to the total number of items to produce, we have the following inequality based on those variables.
x + y > 25
Additionally, you can create a second inequality concerning your budget for materials.
20x + 45y < 675
Moreover, you should also add that both values must not be negative, since you can't produce negative tables.
C. By analyzing the constraints and solving the system, you will find that the feasible region contains 4 vertices.
(0,0)
(18, 7)
(0, 15)
(33.75, 0) or (33, 0) if you prefer to round it.
The diagonal measures 20.68 ft; the shorter base is 17.21 ft. To understand this, we recognize that with base angles summing to 140°, each angle is 70°, given the isosceles trapezoid's properties. We can apply the Law of Cosines to find the diagonal's length, denoted as d. The length of the diagonal determines to be d = 20.68 ft. Determining the shorter base is somewhat more complex. By drawing an altitude from the upper vertices to the base, which measures 22 ft, we create two similar smaller right triangles requiring us to find the height and base measures related to each of the 70-degree angles and the hypotenuse of 7. By working through the calculations for height and base from one triangle, we subsequently find that 22 minus twice the base measure gets us to the shorter base's measure, arriving at x = 17.21 ft.
The slope equals 0 because the y value remains constant, indicating a slope of 0.
