Solve Optimization Problems Using Calculus
1) Start by reviewing the Lesson 2 Commentary, Example 1. Suppose that the truck driver in this example earns $18 per hour. What is the most economical speed for the truck?
a. Solve this first by using calculus.
b. Then solve by using the Solver in Excel.
c. How much would the driver's hourly wage need to be in order for the optimum speed to violate a constraint limiting the speed to 80 mph? This is similar to previous problem except that you are solving for the wage given the speed. In the previous problem you were solving for the speed given the wage. You may use calculus or the Solver in Excel to solve this. As a hint, set the hourly wage to a variable and solve the new equation. Be sure to clearly explain the steps that you are using to solve this problem (and parts a and b too). Your score will be based on how well you explain your solutions.
2) Find the minimum and maximum of the function: f(x) = 4x6 - 2x3 on the interval [-2, 0]. Solve this problem by using calculus and the Solver in Excel. Include an analysis of how your initial guess affects the calculated optimum when using the spreadsheet. Choose at least 10 initial guesses. Do to this, remember that you set the decision variable to a value, run the Solver, and observe what the final objective function value is. Do this once for each of the initial guesses and see if (and by how much) the objective function value changes. Discuss what you observe.