The maximum profit would be $1325. Since they make less profit on deluxe seats, you want to get as few of those as possible. You also want to get as many people on the boat as possible, which is 45. The minimum number of deluxe seats you could sell is 5, so that's what we'll use for the max. profit. They make $25 off of each of those seats so 5 times $25 is $125. That leaves 40 economy seats, with a profit of $30 per seat. You have 40 spots left open, so we'll sell 40 economy seats, which will meet your minimum of 14 economy seats. 40 times $30 is $1200. Add $125 and $1200 to get $1325 and you have your maximum profit!
This can solved graphically, using algebraic manipulation or differential calculus.
Plotting the equation will generate a parabola. The vertex represents the point where the ball will reach the maximum height.
The vertex can be determined by completing the square
h = -16t2 + 45t + 5
h - 5 = -16(t2 - 45/16t)
h - 5 - 2025/64 = -16(t2 - 45/16t + 2025/1024)
(-1/16)(h - 2345/64) = (t - 45/32)^2
The vertex is
(45/32,2345/64) or (1.41,36.64)
The maximum height is 36.64 ft
Using calculus, taking the first derivative of the equation and equating to 0
dh/dt = 0 = -32t + 45
t = 45/32
Substituting this value to the equation
h = -16(45/32)^2 + 45(45/32) + 5
h = 36.64 ft
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Answer: 2/7
Step-by-step explanation:
Slope form: y2-y1/x2-x1
4-8/-4-10 ==> -4/-14 ==> 2/7
C always means the hypotenuse. In that case C=7.2If you are trying to find the missing side length though, it would be about 4.87Hope that helps! :)
