A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by P(x) = -0.001x² + 3x - 1800.

a. What is his maximum profit per day?

b. How many cans must be sold in order to obtain the maximum profit?

Answer:

a. $450

b. 1500 cans

Step-by-step explanation:

Given the following quadratic function;

P(x) = -0.001x² + 3x - 1800 ......equation 1

a. To find his maximum profit per day;

Since P(x) is a quadratic equation, P(x) would be maximum when $x = \frac {-b}{2a}$

Note : the standard form of a quadratic equation is ax² + bx + c = 0 ......equation 2

Comparing eqn 1 and eqn 2, we have;

a = -0.001, b = 3 and c = -1800

Now, we determine the maximum profit;

$x = \frac {-b}{2a}$

Substituting the values, we have;

$x = \frac {-3}{2*(-0.001)}$

Cancelling out the negative signs, we have;

$x = \frac {3}{2*0.001}$

$x = \frac {3}{0.002}$

x at maximum = 1500

Substituting the value of "x" into equation 1;

P(1500) = -0.001 * 1500² + 3(1500) - 1800

P(1500) = -0.001 * 2250000 + 4500 - 1800

P(1500) = -2250 + 2700

P(1500) = $450

b. Therefore, the soft-drink vendor must sell 1500 cans in order to obtain the maximum profit.

5 0

2 years ago

The equation 9(u – 2) + 1.5u = 8.25 models the total miles Michael traveled one afternoon while sledding, where u equals the num

lara31 [8.8K]

Answer:

Solution; u = 2.5

Step-by-step explanation:

We can neglect the information provided to us, besides that of the equation 9(u – 2) + 1.5u = 8.25, as we are only to find the value of u, any other information is not of need;

9(u – 2) + 1.5u = 8.25 ⇒ apply the distributive property on the expression ( u - 2 ), distributing the 9 to the elements inside,

9u - 18 + 1.5u = 8.25 ⇒ add like elements,

10.5u = 26.25, solve for u,

Solution; u = 2.5

4 0

3 years ago

Read 2 more answers

Please help........................

maksim [4K]

Answer:

a. (0,0), (2,0), (4,0)

b. (0,0)

Step-by-step explanation:

To find the x-intercept points, you set the equation equal to 0.

0=x³-6x²+8x [factor out an x]

0=x(x²-6x+8) [factor (x²-6x+8)]

0=x(x-2)(x-4) [set each factor equal to 0]

x=0

x-2=0 [add both sides by 2]

x=2

x-4=0 [add both sides by 4]

x=4

Now, we know our x-intercept points: (0,0), (2,0), (4,0).

To find the y-intercept points, we know that it is located on the y-axis, meaning x=0. We plug in 0 for x, and we will know our y-intercept point.

y=(0)³-6(0)²+8(0) [multiply]

y=0

The y-intercept point is (0,0).

8 0

2 years ago