Linear Programming Problem

Question

Given that the optimal solution of the following linear programming problem is x = 15 and y = 10, State the problem in standard form and do a constraint analysis for the optimal solution. 

Maximize z =  50x + 40y 

Subject to 

4x + 2y ≤ 80 

3x + 5y ≥ 60 

y ≤ 10 

x, y ≥ 0

Question

A. Graph the function ƒ(x) = x^3 – 4x + 2.
B. Find the domain and range of ƒ, showing all work or explaining your rationale.
C. Find the derivative of ƒ, showing all work.
D. Find the slope of the graph of ƒ at x = 0, showing all work.
E. Let ƒ represent the position of an object with respect to time that is moving along a line. Identify when the object is moving in the positive and negative directions and when the object is at rest, showing all work.