Answer:
- <u><em>P = 0.40x + 0.50y</em></u>
Explanation:
The <em>objective function</em> is the function that you want to optimize: usually minimize in the case of costs, and maximize in the case of revenues or profits.
In this case, you know the <em>profits</em> that a manufacturer earns from two types of <em>bottled coffe drinks</em>: <em>cappuccinos</em> and <em>cafés au lait</em>.
Each bottle of <em>cappuccino earns a profit of $0.40</em> and each bottle of <em>café au lait earns a profit of $0.50</em>.
Then:
- using the variable x for the number bottles of cappuccino produced, the profit earned from x bottles is 0.40x, and
- using the variable y for the number of bottles of café au lait the produced, the profit earned from y bottles is 0.5y.
The total profit earned, P, is the sum of the profits earned from each type of bottled coffee drinks:
That is the <em>objective function</em>, i.e. the function that the manufacturer must try to maximize subject to the corresponding constraints.
On a die there are 3 even numbers. We want to know the probability that rolling a die we get 3 or an even number. So there are 4 positive outcomes out of 6.
4/6=2/3
Answer:
x = 144
Step-by-step explanation:
y α x
we introduce a constant 'k' when changing from α to =.
i.e y = kx
y = ⅓ when x = 12
Meaning, ⅓ = k * 12
⅓ = 12k
k = ⅓ ÷ 12
k = 1/36
If y = 4, x = ?
using the equation y = kx
4 = (1/36)x
x = 4 ÷ (1/36)
x = 4 * 36
x = 144
Answer:

And if we count the number of zeros before the number 7, we can rewrite the number like this:

We cansolve this problem also counting the number of positions that we need to move the decimal point to the right in order to obtain the first number (7)
And the best option would be:
B. 7 x 10-7
Step-by-step explanation:
For this case we have the following number given:

And if we count the number of zeros before the number 7, we can rewrite the number like this:

We cansolve this problem also counting the number of positions that we need to move the decimal point to the right in order to obtain the first number (7)
And the best option would be:
B. 7 x 10-7
A. Total Revenue (R) is equal to price per dive (P) multiplied by number of customers (C). We can write
.
Per price increase is $20. So four price increase is $
. Hence, price per dive is 100+80=$180.
Also per price increase, 2 customers are reduced from 30. For 4 price increases,
customers are reduced. Hence, total customers is
.
So Total Revenue is:

B. Each price increase is 20. So x price increase is 20x. Hence, new price per dive would be equal to the sum of 100 and 20x.
Also per price increase, customers decrease by 2. So per x price increases, the customer decrease is 2x. Hence, new number of customers is the difference of 30 and 2x.
Therefor we can write the quadratic equation for total revenue as the new price times the new number of customers.

C. We are looking for the point (x) at which the equation modeled in part (B) gives a maximum value of revenue (y). That x value is given as
, where a is the coefficient of
and b is the coefficient of x. So we have,

That means, the greatest revenue is achieved after 5 price increases. Each price increase was 20, so 5 price increase would be
. So the price that gives the greatest revenue is
.
ANSWERS:
A. $3960
B. 
C. $200