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.
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