Find the maximum of the function: f(x) = 4 + 7x + 2x^2 − x^3 using Golden Section Search with initial conditions: xL = −1 and xU = 4 +27/40 Perform up to 5 iterations.

Differentiate. f(x) = In (4x + 1)(x+7)³ (1 - 6x)5

Please let me know how to find out the answer for (b) using the substitution method. I know how to get the functions for (2) as shown.  Question:  A company can decide how many additional labor hours to acquire for a given week. Subcontractor workers will only work a maximum of 20 hours a week. The company must produce at least 200 units of product A, 300 units of product B, and 400 units of product C. In 1 hour of work, worker 1 can produce 15 units of product A, 10 units of product B, and 30 units of product C. Worker 2 can produce 5 units of product A, 20 units of product B, and 35 units of product C. Worker 3 can produce 20 units of product A, 15 units of product B, and 25 units of product C. Worker 1 demands a salary of $50/hr, worker 2 demands a salary of $40/hr, and worker 3 demands a salary of $45/hr. The company must choose how many hours they should contract with each worker to meet their production requirements and minimize labor cost. (a) Formulate this as a linear…