# Linear programming

Riverside Oil Company in eastern Kentucky produces regular and supreme gasoline. Each barrel of regular sells for \$21 and must have an octane rating of at least 90. Each barrel of supreme sells for \$25 and must have an octane rating of at least 97. Each of these types of gasoline are manufactured by mixing different quantities of the following three inputs:

Input______Cost/barrel__Oct rating__Barrels avbl (in 1000s)
1_________\$17.25__100__150
2_________\$15.75__87__350
3_________\$17.75__110__300

Riverside has orders for 300,000 barrels of regular and 450,000 barrels of supreme. How should the company allocate the available inputs to the production of regular and supreme gasoline if they want to maximize profits?

I just need to figure out the MAX and constraints.

1. 👍 0
2. 👎 0
3. 👁 1,032
1. The constraints and the objective function can be obtained from the instructions and data.

First start off with defining the variables, x1,x2,x3 for the quantity (in 1000's of barrels) of each type of gasoline available for regular product, and x4,x5,x6 for supreme.

Since the company is buying, the quantities x1,x2,... cannot be negative. So constraints are:

x1≥0 (input 1 for regular)
...
x4≥0 (input 1 for supreme)
...

The availability tells us that:
x1+x4≤150
x2+x5≤350
...

The order quantity requirements (in 1000's of barrels)
x1+x2+x3=300
...

The octane requirement is such that the weighted average of the octane level must be greater than 90 and 97 for each type of gasoline. The sums (x1+x2+x3) and (x4+x5+x6) are 300 and 450 respectively:
(100x1+87x2+110x3)/300≥90
...

Profit is selling price - cost, so the objective function is:
P(x1,x2,x3,x4,x5,x6)
=300*\$21-(\$17.25x1+\$15.75x2+\$17.75x3)
+...

Can you take it from here?

1. 👍 0
2. 👎 0
2. Yes, thank you so much.

1. 👍 0
2. 👎 0
3. You're welcome!

1. 👍 0
2. 👎 0
4. That's great formular. Could you create a spreadsheet model for this problem and solve it using Solver?

1. 👍 0
2. 👎 0
5. Is there a spreadsheet model to complete this on excel?

1. 👍 0
2. 👎 0

## Similar Questions

1. ### history

How have petro-economics shaped the Middle East? A. Economic competition among Middle Eastern states to be the top oil producer often becomes bitter. B. Arab nations have consolidated their power by negotiating the purchase of oil

asked by Michael on June 5, 2018
2. ### history

which describes the most accurate reason why oil wealth affects the stability of the middle east? a. wealthier middle eastern countries are able to use their oil profits to fund armies for self-defense. b. middle eastern nations

asked by vanessa on July 11, 2019
3. ### American government

What is the difference between a regular session of Congress and a special session of Congress? A) A regular session has all the members, while a special session only has a few members B) A regular session is for making laws,

asked by Nashaia on October 7, 2016
4. ### Maths

Hi, I need to calculate the size of one of the interior angles of a regular heptagon (i.e. a regular 7-sided polygon). Any help appreciated

asked by Jim on July 12, 2010
5. ### Fitness & Nutrition

16. How does regular exercise help to reduce the effects of mental stress? A. Regular exercise gets you away from the home or office and away from stress. B. Regular exercise has been shown to reduce the physical effects of

asked by Cassie on November 2, 2013
1. ### Geometry / Trig

What is the area of a regular hexagon with a distance from its center to a vertex of 1 cm? (Hint: A regular hexagon can be divided into six equilateral triangles.) hex The area of the regular hexagon is _____ ?

asked by Sosa on January 25, 2017
2. ### Health

13. How does regular exercise help to reduce the effects of mental stress? A. People who regularly exercise are happy people and are fun to be around. B. Regular exercise gives you better mental discipline, so you're better able

asked by Sarah on October 7, 2014
3. ### maths

An employee worked 11 hours in a day. Her regular working day is 7.5 hours and the rest was overtime, for which she was paid 1.5 times her regular hourly rate. If she was paid \$112 for the day, what was her regular rate per hour

asked by Anonymous on October 15, 2015
4. ### Chemistry

Regular gasoline (C8H18) reacts with oxygen gas to form carbon dioxide gas and water vapor. If your tanks of gasoline holds about 10.5 kg of gasoline, how many liters of carbon dioxide are formed at 24 degrees Celcius and 725mm Hg

asked by Linda on April 18, 2012
5. ### Math/Management

FuelMotion is an oil company that owns two oil processing plants that produce gasoline from crude oil. Their Georgia Plant produces 2 thousand gallons of premium, 1 thousand gallons of medium, and 6 thousand gallons of regular

asked by Carla on October 17, 2012