On Saturday, Luke drove 5x − 4 miles. On Sunday, he drove 3x − 3 miles. What is the difference in miles driven?

lawyer [7]

Answer:

Takis in my opinion :))))))

7 0

3 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

What is the correct answer to number 7? Please explain and break it down step by step.

a_sh-v [17]

Answer:

The answer to your question is (x + 3)

Step-by-step explanation:

$\frac{5x + 5}{x} \frac{x^{3}+ 3x^{2}}{x^{2} - 1} \frac{x - 1}{5x}$

Factor the expression

$\frac{5(x + 1)}{x} \frac{x^{2}(x + 3)}{(x - 1)(x + 1)} \frac{x - 1}{5x}$

Simplify

Cancel 5 because is in both numerator and denominator

Cancel (x + 1) because is in both numerator and denominator

Cancel (x - 1) because is in both numerator and denominator

Cancel x² because is in both numerator and denominator

After simplifying, the result is (x + 3)

6 0

3 years ago

A laptop computer is purchased for $2700. Each year, it’s value is 70% of its value the year before after how many years will la

n200080 [17]

Answer: 5 years!

Reasoning:

Year 1: 2700 x .70=1890

Year 2: 1890 x .70= 1323

Year 3: 1323 x .70= 926.1

Year 4: 926.1 x .70= 648.27

Year 5: 648.27 x .70=453.79

3 0

3 years ago

In the graph below, the area above f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where

drek231 [11]

Answer: OPTION C.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

Notice that the line of f(x) is dashed. This means that the symbol of the inequality must be or $>$ .

Since the shaded region A is above the line, the symbol is $>$

Observe that its y-intercept is:

$b=3$

The line of g(x) is solid. This means that the symbol of the inequality must be $\leq$ or $\geq$ .

Since the shaded region B is below the line, the symbol is $\leq$ .

Observe that its y-intercept is:

$b=-2$ .

Based on this, we can conclude that the graph represents the following System of Inequalities:

$\left \{ {{y\leq 2x -2} \atop {y >-x + 3}} \right.$

8 0

3 years ago