Answer:
Selling 40 items will produce a maximum profit.
Step-by-step explanation:
We need to use First and Second Derivative Tests on profit function to determine how many items will lead to maximum profit. Let , where is the profit for a product, measured in US dollars, and is the amount of items, dimensionless.
First we derive the profit function and equalize it to zero:
(Eq. 1)
Roots are found by Quadratic Formula:
and
Only the first root may offer a realistic solution. The second derivative of the profit function is found and evaluated at first root. That is:
(Eq. 2)
(Absolute maximum)
Therefore, selling 40 items will produce a maximum profit.
The final answer is (2,1).
Step 1: Solve for either x or y in one of the two equations.
x + 3y = 5
- 3y - 3y
----------------------
x = -3y + 5
Step 2: Substitute the expression you got for x into the opposite equation.
-3y + 5 - 3y = -1
-6y + 5 = -1
- 5 - 5
--------------------
-6y = -6
------ -----
-6 6
y = 1
Step 3: Plug in the solution you got for y into either of the 2 equations.
x + 3(1) = 5
x + 3 = 5
- 3 - 3
---------------
x = 2
Answer:
16 and -16
Step-by-step explanation:
Let's break it down.
You spent $20. Plus the $1 tip.
20 - 1 = 19
$19 is how much you spent without the tip
The cost for the taxi ride itself is $3
19 - 3 = 16
$16 is how much you spent without the ride cost + tip
You spent $2 for every mile traveled.
16/2=8
You traveled 8 miles