Exam 7: Nonlinear Optimization Models

Solver is guaranteed to find the global minimum (if it exists) if the objective function is concave and the constraints are linear.

Exhibit 7-1A company manufactures two products. If it charges price p1 for product 1 and price p2 for product 2, it can sell quantities q1 = 55 − 3p1 + 2p2 and q2 = 75 + 2p1 − 2p2 for products 1 and 2, respectively. It costs the company $20 to produce a unit of product 1 and $65 to produce a unit of product 2. -Refer to Exhibit 7-1. How many units of each product should the company produce? What prices should it charge, to maximize profit?

Which of the following is not one of the conditions for maximization in a nonlinear problem?

Solver is guaranteed to solve certain types of nonlinear programming models.

Exhibit 7-3A company has the following historical data on the number of ad exposures and the corresponding number of units sold of one of its products: \ Historical Ads Units 0 3 20 18 40 34 60 46 80 56 100 65 120 72 140 78 160 82 180 85 200 90 220 90 240 93 260 94 280 95 300 101 320 98 340 100 360 98 380 101 400 105 -[Part 1] Refer to Exhibit 7-3. Formulate a nonlinear optimization model to find the parameters of a function of the form: f(x) = axb to model demand for its product as a function of ad exposures (x).

Which of the following is not one of the reasons an optimization model can become nonlinear?

A function is concave if:

Relative to linear optimization models, nonlinear optimization models are typically more difficult to solve.

In some nonlinear models, Solver will find the optimal solution only if the starting solution is reasonably close to the optimal solution.

The sum of two concave functions is concave.