Exam 7: Nonlinear Optimization Models

Exhibit 7-4 You are given the following means, standard deviations, and correlations for the annual return on three stocks. The means are 0.08, 0.10, and 0.15. The standard deviations are 0.15, 0.20, and 0.30. The correlation between stocks 1 and 2 is 0.62, between stocks 1 and 3 is 0.32, and between stocks 2 and 3 is 0.43. -[Part 1] Refer to Exhibit 7-4.Determine the minimum variance portfolio that yields an expected annual return of at least 0.10

Exhibit 7-4 You are given the following means, standard deviations, and correlations for the annual return on three stocks. The means are 0.08, 0.10, and 0.15. The standard deviations are 0.15, 0.20, and 0.30. The correlation between stocks 1 and 2 is 0.62, between stocks 1 and 3 is 0.32, and between stocks 2 and 3 is 0.43. -[Part 2] Refer to Exhibit 7-4.Determine the minimum variance portfolio that yields an expected annual return of at least 0.12.How has the portfolio changed from your answer in Part 1

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

Exhibit 7-4 You are given the following means, standard deviations, and correlations for the annual return on three stocks. The means are 0.08, 0.10, and 0.15. The standard deviations are 0.15, 0.20, and 0.30. The correlation between stocks 1 and 2 is 0.62, between stocks 1 and 3 is 0.32, and between stocks 2 and 3 is 0.43. -Refer to Exhibit 7-4.Suppose you set the weights in the portfolio to a maximum of 0.45 for each stock.Is it possible to achieve a 12% return What is the portfolio standard deviation in that case

In pricing models,elasticity of demand is an input with specifies the:

Exhibit 7-1 A 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.Suppose the company is required by regulation to charge the same price for both products.How many units of each product should the company produce in that case What prices should it charge,to maximize profit

Exhibit 7-3 A 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 2] Refer to Exhibit 7-3.Formulate a nonlinear optimization model to find the parameters of a function of the form: f(x)= a(1 − e−bx)to model demand for its product as a function of ad exposures (x).In terms of fit,is this model better or worse than the model in Part 1 Explain your answer

Exhibit 7-1 A 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

Exhibit 7-2 A soda producer makes and sells two products, Classic Cola and Diet Cola. During the planning period, if the producer spends x1 dollars on promotion of Classic Cola, it can sell 100x10.5 cases of Classic Cola, and if it spends x2 dollars on promotion of Diet Cola, it can sell 10x20.75 cases of Diet Cola. Each case of Classic Cola sells for $12.00 and costs $0.95 to produce and ship to customers, while each case of Diet Cola sells for $12.50 and costs $1.00 to produce and ship to customers. A total of $7,500 is available for promotion during the planning period. -Refer to Exhibit 7-2.Formulate and solve a nonlinear optimization model to help this soda producer identify the best promotional strategies for its two products.

Exhibit 7-3 A 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).