1. The area of a parking lot is 600 square meters. A car requires 6 square meters and a bus requires 30 square meters of

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1. The area of a parking lot is 600 square meters. A car
requires 6 square meters and a bus requires 30 square meters of
space. There should be a space allocated for at least 5 buses. The
lot can handle a maximum of 60 combined vehicles. The parking lot
charges a bus $8 and a car $3 per hour. How many of each type of
vehicle can be parked in the lot to maximize the amount of money
collected? Solution: Objective Uncontrollable Variable (parameters)
Controllable Variable (unknowns) The LP Model: The Solution:
2. A sporting goods manufacturer produces skateboards and
in-line skates. Its dealers demand at least 30 skateboards per day
and 20 pairs of in-line skates per day. The factory can make at
most 60 skateboards and 40 pairs of in-line skates per day. In
addition, the maximum production from skateboards and pairs of
in-line skates cannot exceed 90 units for stocking purposes. The
profit on each skateboard is $12 and the profit on each pair of
in-line skates is $18. How many of each product should the company
manufacture to get the maximum profit. Solution: Objective
Uncontrollable Variable (parameters) Controllable Variable
(unknowns) The LP Model: The Solution:
3. A company makes three types of candy and packages them in
three assortments. Assortment I contains 4 sour, 4 lemon, and 12
lime candies, and sells for $9.40. Assortment II contains 12 sour,
4 lemon, and 4 lime candies, and sells for $7.60. Assortment III
contains 8 sour, 8 lemon, and 8 lime candies, and sells for $
11.00. Manufacturing costs per piece of candy are $0.20 for sour,
$0.25 for lemon, and $ 0.30 for lime. They can make 5,200 sour,
3,800 lemon, and 6,000 lime candies weekly. How many boxes of each
type should the company produce each week in order to maximize its
profit? What is the maximum profit? Notes: 1- You have to calculate
the cost of each assortment 2- The constraints are on the sour,
lime and lemon not the assortments Solution: Objective
Uncontrollable Variable (parameters) Controllable Variable
(unknowns) The LP Model: The Solution:
4. Advertising alternatives for a company include television,
radio, and newspaper. The table below shows the costs and estimates
of audience coverage for each type of media. Cost per advertisement
Audience per advertisement Television $2000 100,000 Newspaper $600
40,000 Radio $300 18,000 The newspaper limits the number of weekly
advertisements from a single company to ten. Moreover, to balance
the advertising among the three types of media, no more than half
of the total number of advertisements should occur on the radio,
and at least 10% should occur on television. The weekly advertising
budget is $18,200. How many advertisements should run in each of
the three types of media to maximize the total audience (exposure)?
Solution: Objective Uncontrollable Variable (parameters)
Controllable Variable (unknowns) The LP Model: The Solution: