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Exam 16: Nonlinear and Non-Smooth Optimization

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Question 31

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Use the table below to answer the following question(s) . Shirley Templeton is a real estate agent for Paralol Realty.Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows.These 5 bungalows are situated in close proximity.In order to make traveling easire, Shirley decides to move to a location closer to the 5 bungalows.The table below gives the location (X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow.Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $\begin{array}{l}\text { Bungalow Location }\\\begin{array}{|l|l|l|l}\hline & & & \\\hline \text { Data } & \text { X-coordinate } & Y \text {-coordinate } & \text { Trips/Month } \\\hline \text { Location } & 0 & 0 & 6 \\\hline \text { Bungalow 1 } & 25 & 100 & 30 \\\hline \text { Bungalow 2 } & 20 & 75 & 15 \\\hline \text { Bungalow 3 } & 90 & 80 & 28 \\\hline \text { Bungalow 4 } & 60 & 100 & 10\end{array}\end{array}$ -According to the model, what is the X-coordinate for the location of Shirley's new accommodation?

A) 54.62
B) 36.53
C) 25
D) 23.12

E) All of the above
F) B) and D)

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Question 32

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Explain how the Markowitz portfolio model is a quadratic optimization model.

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The Markowitz portfolio model is a class...

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Question 33

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Use the table below to answer the following question(s) . Jonathan Reese is considering three stocks in which to invest with a fixed budget.The table below provides information on Jonathan's expected returns for each stock.The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks.He expects a total return of at least 10%. Develop a quadratic optimization model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix. -According to the model, what is the expected total return on all stocks?

Use the table below to answer the following question(s) . Shirley Templeton is a real estate agent for Paralol Realty.Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows.These 5 bungalows are situated in close proximity.In order to make traveling easire, Shirley decides to move to a location closer to the 5 bungalows.The table below gives the location (X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow.Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $\begin{array}{l}\text { Bungalow Location }\\\begin{array}{|l|l|l|l}\hline & & & \\\hline \text { Data } & \text { X-coordinate } & Y \text {-coordinate } & \text { Trips/Month } \\\hline \text { Location } & 0 & 0 & 6 \\\hline \text { Bungalow 1 } & 25 & 100 & 30 \\\hline \text { Bungalow 2 } & 20 & 75 & 15 \\\hline \text { Bungalow 3 } & 90 & 80 & 28 \\\hline \text { Bungalow 4 } & 60 & 100 & 10\end{array}\end{array}$ -According to the model, what is the Y-coordinate for the location of Shirley's new accommodation?

Use the table below to create a nonlinear model based on the table to answer the following question(s) . The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues.They have three classes of tickets: Classic, Silver, and Gold.The table below provides information on the average ticket sales, revenue and price elasticity on demand.They have a total seating capacity of 300.The table also provides the price range within which they plan to reduce their ticket rates. -According to the nonlinear model, which of the following is the projected sales figure for Gold tickets at the new price?

All quadratic optimization models have nonlinear constraints.

According to the model, which of the following is the weighted distance between the phone charger and Testing cell?

Use the table below to answer the following question(s) . Jonathan Reese is considering three stocks in which to invest with a fixed budget.The table below provides information on Jonathan's expected returns for each stock.The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks.He expects a total return of at least 10%. Develop a quadratic optimization model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix. -According to the model, what percentage of the budget should be allocated to Stock 2?

Use the table below to answer the following question(s) . Shirley Templeton is a real estate agent for Paralol Realty.Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows.These 5 bungalows are situated in close proximity.In order to make traveling easire, Shirley decides to move to a location closer to the 5 bungalows.The table below gives the location (X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow.Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $\begin{array}{l}\text { Bungalow Location }\\\begin{array}{|l|l|l|l}\hline & & & \\\hline \text { Data } & \text { X-coordinate } & Y \text {-coordinate } & \text { Trips/Month } \\\hline \text { Location } & 0 & 0 & 6 \\\hline \text { Bungalow 1 } & 25 & 100 & 30 \\\hline \text { Bungalow 2 } & 20 & 75 & 15 \\\hline \text { Bungalow 3 } & 90 & 80 & 28 \\\hline \text { Bungalow 4 } & 60 & 100 & 10\end{array}\end{array}$ -Given that Q = order quantity, D = annual demand, C = unit cost of the item, C₀ = cost per order placed, i = inventory carrying charge per unit, which of the following represents the holding cost per unit?

Use the table below to create a nonlinear model based on the table to answer the following question(s) . The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues.They have three classes of tickets: Classic, Silver, and Gold.The table below provides information on the average ticket sales, revenue and price elasticity on demand.They have a total seating capacity of 300.The table also provides the price range within which they plan to reduce their ticket rates. -According to the nonlinear model, which of the following is the projected revenue figure for Classic tickets based on its new price?

Use the table below to create a nonlinear model based on the table to answer the following question(s) . The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues.They have three classes of tickets: Classic, Silver, and Gold.The table below provides information on the average ticket sales, revenue and price elasticity on demand.They have a total seating capacity of 300.The table also provides the price range within which they plan to reduce their ticket rates. -According to the nonlinear model, which of the following is the projected revenue figure for Silver tickets based on its new price?

According to the model, which of the following is the weighted distance between the phone charger and Paint cell?

Explain the travelling salesperson problem with examples.

Use the table below to answer the following question(s) . Jonathan Reese is considering three stocks in which to invest with a fixed budget.The table below provides information on Jonathan's expected returns for each stock.The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks.He expects a total return of at least 10%. Develop a quadratic optimization model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix. -According to the model, what is the squared term value for Stock 2 variance?

According to the model, what is the total weighted distance between the 5 production cells and the phone charger?

Use the table below to answer the following question(s) . Shirley Templeton is a real estate agent for Paralol Realty.Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows.These 5 bungalows are situated in close proximity.In order to make traveling easire, Shirley decides to move to a location closer to the 5 bungalows.The table below gives the location (X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow.Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $\begin{array}{l}\text { Bungalow Location }\\\begin{array}{|l|l|l|l}\hline & & & \\\hline \text { Data } & \text { X-coordinate } & Y \text {-coordinate } & \text { Trips/Month } \\\hline \text { Location } & 0 & 0 & 6 \\\hline \text { Bungalow 1 } & 25 & 100 & 30 \\\hline \text { Bungalow 2 } & 20 & 75 & 15 \\\hline \text { Bungalow 3 } & 90 & 80 & 28 \\\hline \text { Bungalow 4 } & 60 & 100 & 10\end{array}\end{array}$ -According to the model, what is the distance between Shirley's new accommodation and Bungalow 3?

Use the table below to create a nonlinear model based on the table to answer the following question(s) . The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues.They have three classes of tickets: Classic, Silver, and Gold.The table below provides information on the average ticket sales, revenue and price elasticity on demand.They have a total seating capacity of 300.The table also provides the price range within which they plan to reduce their ticket rates. -Which of the following is true of the nonlinear model created for the Atlas movie ticket repricing scenario?

Use the table below to create a nonlinear model based on the table to answer the following question(s) . The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues.They have three classes of tickets: Classic, Silver, and Gold.The table below provides information on the average ticket sales, revenue and price elasticity on demand.They have a total seating capacity of 300.The table also provides the price range within which they plan to reduce their ticket rates. -According to the nonlinear model, which of the following is the projected sales figure for Classic tickets at the new price?

According to the model, which of the following is the weighted distance between the phone charger and Measurements cell?

Use the table below to create a nonlinear model based on the table to answer the following question(s) . The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues.They have three classes of tickets: Classic, Silver, and Gold.The table below provides information on the average ticket sales, revenue and price elasticity on demand.They have a total seating capacity of 300.The table also provides the price range within which they plan to reduce their ticket rates. -According to the nonlinear model, which of the following is the total projected revenue for the new sales figures?