Suppose we have a function f(x) = 2x^3 – 5x^2 + 3x – 1, and a line L defined by y = mx + b. What is the slope m of the line L such that the line is tangent to the graph of f(x) at the point where x = 2?
A manufacturing company produces two types of products, A and B. Each unit of A requires 3 hours of labor and 4 hours of machine time, while each unit of B requires 4 hours of labor and 5 hours of machine time. The company has 3000 hours of labor available and 4000 hours of machine time available. If the profit for each unit of A is $10 and the profit for each unit of B is $15, how many units of each product should the company produce in order to maximize their profit, and what is the maximum profit?
