Graph a graph b graph c

Need help ASAP! Tysm

UNO [17]

Answer:

The answer is B) -29.

Step-by-step explanation:

3 0

4 years ago

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) Optimal solution: 40.000 units of R and 10.000 of PC = $17.000

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

d) Binding Constaints:

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

3 years ago

This is due tomorrow and PLEASE HELP ME ON THESE QUESTIONS! THIS IS DUE TOMORROW!

Usimov [2.4K]

3: multiply the change per minute by how many minutes: 3.1x15=46.5. 5: Is your opinion, I can't tell you how to feel. But a negative times a negative is a positive, so if there is an even number of negatives no matter how many positives there are it will be positive, if there is an odd number of negatives it will be negative. :) Hope this helps!

4 0

3 years ago

A group of college students are going to a lake house for the weekend and plan on renting small cars and large cars to make the

maxonik [38]

The students rented 4 small cars and 8 large cars.

Step-by-step explanation:

Given,

Number of people in small car = 4

Number of people in large car = 7

Total people in both type of cars = 72

Let,

x represent the number of small cars rented.

y represent the number of large cars rented.

According to given statement;

4x+7y=72 Eqn 1

y = 2x Eqn 2

Putting value of y from Eqn 2 in Eqn 1

$4x+7(2x)=72\\4x+14x=72\\18x=72$

Dividing both sides by 18

$\frac{18x}{18}=\frac{72}{18}\\x=4$

Putting x=4 in Eqn 2

$y=2(4)\\y=8$

The students rented 4 small cars and 8 large cars.

Keywords: linear equation, substitution method

Learn more about linear equations at:

#LearnwithBrainly

3 0

3 years ago

An expression is shown below:

PolarNik [594]

Notation
I imagine that the expression you are asked to work with is:
$3 x^{3}y+15xy-9 x^{2} y-45y$

When you use a keyboard it is customary to use "^" to denote an exponent is coming so you could have written: 3x^3y+15xy-9x^2y-45y just to be clear.

PART A
To factor out the GCF we are looking for the greatest factor among the terms. Looking at the coefficients (the numbers) the largest number they can all be divided by is 3 so we will pull out a 3. Notice also that each term has a y in it so we can pull out that.

This gives us: $3 x^{3}y+15xy-9 x^{2} y-45y=3y( x^{3}+5x-3 x^{2} -15)$

To factor is to write as a product (something times something else). It undoes multiplication so in this case if you take what we got and multiplied it back you should get the expression we started with.

PART B
Start with the answer in part A. Namely, $3y( x^{3}+5x-3 x^{2} -15)$ . For now let's focus only on what is in the parenthesis. We have four terms so let's take them two at a time. I am separating the expression in two using square brackets. $[( x^{3}+5x)]-[3 x^{2} -15]$

Let's next factor what is in each bracket:
$[( x^{3}+5x)]-[3 x^{2} -15] = [x( x^{2} +5)]-[3( x^{2} +5)]$

Notice that both brackets have the same expression in them so now we factor that out: $[x( x^{2} +5)]-[3( x^{2} +5)] = (x-3)( x^{2} +5)$

Our original expression (the one we started the problem with) had a 3y we already pulled out. We need to include that in the completely factored expression. Doing so we get: $3 x^{3}y+15xy-9 x^{2} y-45y =(3y) (x-3)( x^{2} +5)$

8 0

3 years ago