Answer:
A = (100 - y)y
Maximum area = 2500 sq. feet.
Step-by-step explanation:
Let the length of the combined rectangular area is y feet and the shared width is x feet.
So, perimeter of the two rectangle together is (3x + 2y) = 200 {Given}
⇒ 2y = 200 - 3x
⇒
...... (1).
a) Now, area of the total plot in sq. feet is
........ (2)
So, this is the expression for area A in terms of length of shared side x.
b) For area to be maximum the condition is ![\frac{dA}{dx} = 0](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdx%7D%20%3D%200)
Now, differentiating equation (2) on both sides with respect to x we get
![\frac{dA}{dx} = 100 - 3x = 0](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdx%7D%20%3D%20100%20-%203x%20%3D%200)
⇒ x = 33.33 feet.
So, from equation (1) we get ![y= \frac{1}{2} (200 - 3x)](https://tex.z-dn.net/?f=y%3D%20%5Cfrac%7B1%7D%7B2%7D%20%28200%20-%203x%29)
⇒ x = 50 feet.
So, the value of maximum area = 50 × 33.33 = 1666.5 sq. feet. (Answer)
9514 1404 393
Answer:
- f(x) = -0.15x^2 +19.8x -11 . . . profit function
- $642.40 maximum daily profit
- 66 gallons sold
- $10.90 per gallon
Step-by-step explanation:
<u>Given</u>:
daily cost function c(x) = x +11
price-demand function p(x) = -0.15x +20.8
<u>Find</u>:
daily profit function
maximum daily profit
quantity sold for maximum profit
price for maximum profit
<u>Solution</u>:
The revenue is the product of price and demand:
x·p(x) = -0.15x^2 +20.8x
The profit is the difference between revenue and cost:
f(x) = x·p(x) -c(x) = -0.15x^2 +20.8x -x -11
f(x) = -0.15x^2 +19.8x -11 . . . . . daily profit function
__
The maximum profit will be had a the vertex of the curve, found where ...
x = -(19.8)/(2(-0.15)) = 66
f(66) = (-0.15·66 +19.8)66 -11 = 9.9·66 -11 = 642.40
The maximum profit is $642.40, when 66 gallons of ice cream are sold.
__
The price that will result in demand of 66 gallons of ice cream is ...
p(66) = -0.15(66) +20.8 = 10.9
The price to charge per gallon to maximize profit is $10.90.
Answer:
80:120
Step-by-step explanation:
20 x 4 = 80
30 x 4 = 120
Answer: answers 12 m
Step-by-step explanation:
took the test
Your middle finger and index/pointer.