Linear Programming
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Last updated over 3 years ago
10 questions
Basics
Required
1
Enter the ordered pair to maximize Z:4x+y≤16x≥23y-x≤1212y+9x=Z
Enter the ordered pair to maximize Z:
4x+y≤16
x≥2
3y-x≤12
12y+9x=Z
Required
1
Enter the ordered pair to maximize P:3x+6y≤50y≥44x-3y≥82x+8y=P
Enter the ordered pair to maximize P:
3x+6y≤50
y≥4
4x-3y≥8
2x+8y=P
Required
1
What is the minimum of D?x+y≤18y≥26x-y≤3x≥05x-2y=D
What is the minimum of D?
x+y≤18
y≥2
6x-y≤3
x≥0
5x-2y=D
Required
1
Enter the ordered pair to maximize K. Round to 3 decimal places.4x+8y≤501/2x-1/3y≥3x≤123x+9y=K
Enter the ordered pair to maximize K. Round to 3 decimal places.
4x+8y≤50
1/2x-1/3y≥3
x≤12
3x+9y=K
Required
1
List all vertices of the fesiable region. Round to 3 decimal places and separate your answers by semicolons.4x-y≤20y≥37y+2x≥18x≥0
List all vertices of the fesiable region. Round to 3 decimal places and separate your answers by semicolons.
4x-y≤20
y≥3
7y+2x≥18
x≥0
Word Problems
Required
1
Max is preparing for a bake sale. A dozen cookies take 1 hour to make and produce a profit of $8. A half dozen cupcakes take 3 hours to make but profit $12. He only has 40 hours to bake before the sale, and wants at least 15 things for sale. He also wants to sell at least 8 packs of 6 cupcakes. Graph.
Max is preparing for a bake sale. A dozen cookies take 1 hour to make and produce a profit of $8. A half dozen cupcakes take 3 hours to make but profit $12. He only has 40 hours to bake before the sale, and wants at least 15 things for sale. He also wants to sell at least 8 packs of 6 cupcakes. Graph.
Required
1
How much should he sell to maximize profit?
_______ packs of cupcakes
_______ dozen cookies
1
Lenny owns a lawnmowing buisness. Sam is very efficent and can 3 lawns every hour. He gets paid $17 an hour. Josie can mow 2 lawns every hour. She is paid $12 an hour. Lenny needs to mow at least 20 lawns a week. Each employee has to work at least 2 hours every week. How many hours should he give Josie to minimize his costs?
Lenny owns a lawnmowing buisness. Sam is very efficent and can 3 lawns every hour. He gets paid $17 an hour. Josie can mow 2 lawns every hour. She is paid $12 an hour. Lenny needs to mow at least 20 lawns a week. Each employee has to work at least 2 hours every week. How many hours should he give Josie to minimize his costs?
1
Nia makes jewelry. She takes 2 hours to make a necklace and 1 hour to make a bracelet. Each necklace profits $20 and each bracelet profits $10. She needs to make a total of $400. She also needs to have at least as many necklaces as bracelets. Nia only has room to display 30 items. What is the least amount of hours that Nia can work and still make $400?
Nia makes jewelry. She takes 2 hours to make a necklace and 1 hour to make a bracelet. Each necklace profits $20 and each bracelet profits $10. She needs to make a total of $400. She also needs to have at least as many necklaces as bracelets. Nia only has room to display 30 items. What is the least amount of hours that Nia can work and still make $400?
1
Alexis makes cars. Each sedan takes 5 hours to make and 2 hours to paint. A truck takes 8 hours to make and 4 hours to paint. She has 90 hours to build and 40 hours to paint. A sedan profits $4,500 and a truck profits $6,000. How many sedans and trucks should she make to maximize profit?
_______ sedans
_______ trucks