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gavmur [86]
3 years ago
15

You, your friend, and your cousin play a game. Your friend scores 161 fewer points than you. Your cousin scores 213 more points

than your friend. What is each players score? Who wins?
Mathematics
1 answer:
erik [133]3 years ago
7 0
The correct answer is -52
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Southern Oil Company produces two grades of gasoline: regular and premium. The profit contributions are $0.30 per gallon for reg
Contact [7]

Answer:

a) MAX--> PC (R,P) = 0,3R+ 0,5P

b) <u>Optimal solution</u>: 40.000 units of R and 10.000 of PC = $17.000

c) <u>Slack variables</u>: S3=1000, is the unattended demand of P, the others are 0, that means the restrictions are at the limit.

d) <u>Binding Constaints</u>:

1. 0.3 R+0.6 P ≤ 18.000

2. R+P ≤ 50.000

3. P ≤ 20.000

4. R ≥ 0

5. P ≥ 0

Step-by-step explanation:

I will solve it using the graphic method:

First, we have to define the variables:

R : Regular Gasoline

P: Premium Gasoline

We also call:

PC: Profit contributions

A: Grade A crude oil

• R--> PC: $0,3 --> 0,3 A

• P--> PC: $0,5 --> 0,6 A

So the ecuation to maximize is:

MAX--> PC (R,P) = 0,3R+ 0,5P

The restrictions would be:

1. 18.000 A availabe (R=0,3 A ; P 0,6 A)

2. 50.000 capacity

3. Demand of P: No more than 20.000

4. Both P and R 0 or more.

Translated to formulas:

Answer d)

1. 0.3 R+0.6 P ≤ 18.000

2. R+P ≤ 50.000

3. P ≤ 20.000

4. R ≥ 0

5. P ≥ 0

To know the optimal solution it is better to graph all the restrictions, once you have the graphic, the theory says that the solution is on one of the vertices.

So we define the vertices: (you can see on the graphic, or calculate them with the intersection of the ecuations)

V:(R;P)

• V1: (0;0)

• V2: (0; 20.000)

• V3: (20.000;20.000)

• V4: (40.000; 10.000)

• V5:(50.000;0)

We check each one in the profit ecuation:

MAX--> PC (R,P) = 0,3R+ 0,5P

• V1: 0

• V2: 10.000

• V3: 16.000

• V4: 17.000

• V5: 15.000

As we can see, the optimal solution is  

V4: 40.000 units of regular and 10.000 of premium.

To have the slack variables you have to check in each restriction how much you have to add (or substract) to get to de exact (=) result.  

3 0
2 years ago
Ik this is easy but i forgot how to do it help​
REY [17]

Answer:

7x

Step-by-step explanation:

4+3= 7

=7x

(since they both have the variable "x" we can combine them both)

have a good day! <3

8 0
3 years ago
Subtract: (3m2 + 2n) – (m2 + 2n)
maksim [4K]
The negative in front of the second bracket means that it's times by -1 so each of their signs switches: 
3m^2+2n-m^2-2n 
Add like terms 
2m^2 
the 2n cancels out 
8 0
3 years ago
Read 2 more answers
Among all pairs of numbers whose sum is 100, find a pair whose product is as large as
miv72 [106K]

Answer:

99+1

Step-by-step explanation:

8 0
2 years ago
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Which one is greater -3 5/8 or -3 2/3
Anvisha [2.4K]

Answer:

-3 2/3

Step-by-step explanation:

Find LCM of fractions by first converting them from mixed fraction to improper fraction

6 0
3 years ago
Read 2 more answers
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