辅导BUS 336、讲解Java/Python Marketing Optimization 程序

Assignment 1

BUS 336 - Due In Class Wednesday, January 23, 2019

Question 1: Marketing Optimization

Pepsi needs to decide how many TV advertisements or magazine ads to run during the next quarter (Q2)

of 2019. Each TV ad costs $5,000 and is expected to increase sales by 250,000 bottles. Each magazine ad

costs $2000 and is expected to increase sales by 450,000 bottles. Pepsi has a total budget of $100,000 for

advertising (TV and magazine ads), and wants to spend no more than $70,000 on TV spots and $50,000

on magazine ads. Pepsi also earns a profit of $0.05 on each bottle that it sells! Management would like to

ideally maximize the number of total bottles sold.

a) Formulate a linear program model for this problem. What is the equation to be optimized?

b) Sketch the feasible region for the model. What are the corner points? Show all constraints.

c) Find the optimal solution using the corner points. I.e. How many ad units should be bought?

Question 2: Mining Optimization

Goldcorp extracts minerals from ore mined at two different sites in Argentina. Each ton of ore type 1

contains 20% gold, 20% copper, and 15% molybdenum. On the other hand, each ton of ore type 2

contains 30% gold, 25% copper, and 10% molybdenum. Ore type 1 costs $90 per ton, and ore type 2

costs $120 per ton. Goldcorp would like to buy enough ore to extract at least 8 tonnes of gold, 6 tonnes

of copper, and 5 tonnes of molybdenum in the least costly manner.

a) Formulate a linear program model for this problem. What is the equation to be optimized?

b) Sketch the feasible region for the model. What are the corner points? Show all constraints.

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c) Find the optimal solution using the corner points. I.e. How many tonnes of type 1 ore and type 2

ore should be mined daily to hit their production targets?

Question 3 – Farming Optimization

Farming is big business around the world, and is driven significantly by optimization modelling. Let us

imagine a farm, in California, is 100 acres in total on which the farmers can plant either watermelons or

cantaloupes. Every acre planted with watermelons requires 50 gallons of water per day, and must be

prepared for planting with 20 pounds of fertilizer. On the other hand, every acre planted with

cantaloupes requires 75 gallons of water per day and must be prepared for planting with 15 pounds of

fertilizer. The farmer estimates that it will take 2 hours of labor to harvest each acre planted with

watermelons, and 2.5 hours to harvest each acre planted with cantaloupes. He believes that

watermelons will sell for about $3 each and cantaloupes will sell for about $1 each. Every acre planted

with watermelons is expected to yield 90 salable units while every acre planted with cantaloupes is

expected to yield 300 salable units. The farmer can pump about 6,000 gallons of water per day for

irrigation purposes. He can also buy as much fertilizer as he needs, at a cost of $10 for a 50 pound bag.

Finally, the farmer can hire laborers to harvest the fields at a rate of $5 / hour. If the farmer sells all the

watermelons and cantaloupes he produces, how many acres of each crop should the farmer plant to

maximize profits?

a) Formulate a linear program model for this problem. What is the equation to be optimized?

b) Sketch the feasible region for the model. What are the corner points? Show all constraints.

c) Find the optimal solution using the corner points. I.e. How many acres of each plant should be

farmer to maximize profit?

Question 4 - Advertising Optimization

Ford is evaluating their marketing plan for sedans, SUV’s, and trucks they produce. A TV ad featuring this

a feature SUV has been produced to support this. The company estimates that each showing of this

advertisement will cost $500,000 and increase sales of SUV’s by 3%, but reduce sales of trucks by 1% and

have no effect on the sales of sedans.

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The company has also prepared a second type of advertisements – print ads. This print ad campaign could

run nationally in newspapers and magazines at a cost of $750,000 per title. It is estimated that each

magazine title the ad runs will increase the sales of sedans, SUV’s, and trust by 2%, 1%, and 4%

respectively. The company would like to increase sales of sedans, SUV’s, and trucks by AT LEAST 3%, 14%

and 4% in the least costly manner.

a) Formulate a linear program model for this problem. What is the equation to be optimized?

b) Sketch the feasible region for the model. What are the corner points? Show all constraints.

c) Find the optimal solution using the corner points. I.e. How many ads of each type should be run

in order to generate the increase in the sales of sedans, SUV’s and trucks in the least costly way.