The revenue, in thousands of dollars, of a new flavor of liquor is given below as function of the number of gallons (in hundreds
), x, sold:
What is the maximum revenue? Use units
What is the maximum revenue? Use units
1 answer:
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Try this solution:
Answer: 6 & 4.5 (m-per-h)
Step-by-step explanation:
- The basic formula used in this task is S=V*t, where S - distance, V - speed, t - time.
- the downstream speed is: V+Vc, where V - the speed of the boat in still water, Vc - the speed of the current.
- the upstream speed is: V-Vc.
- according to the described above the distance for downstream is S1=(V+Vc)*t1, where t1=10; the distance for upstream is S2=(V-Vc)*t2, where t2=70.
- for whole travel down- and upstream: S=S1+S2.
- Using these it is possible to make up the system of the equations:
V - the speed of the boat in still water - 6 miles per hour, Vc - the speed of the current - 4.5 miles per hour. All the details for the system of the equations are in the attachment.
Answer:
2.67 inches.
Step-by-step explanation:
Assuming that we represent the size of the squares with the letter y, such that after the squares are being cut from each corner, the rectangular length of the box that is formed can now be ( 23 - 2y), the width to be (13 - 2y) and the height be (x).
The formula for a rectangular box = L × B × W
= (23 -2y)(13-2y) (y)
= (299 - 46y - 26y + 4y²)y
= 299y - 72y² + 4y³
Now for the maximum volume:
dV/dy = 0
This implies that:
299y - 72y² + 4y³ = 299 - 144y + 12y² = 0
By using the quadratic formula; we have :
where;
a = 12; b = -144 and c = 299
Since the width is 13 inches., it can't be possible for the size of the square to be cut to be 9.33
Thus, the size of the square to be cut out from each corner to obtain the maximum volume is 2.67 inches.