1.) Hercules Films is deciding on the price of the video release of its film Bri
ID: 2846838 • Letter: 1
Question
1.) Hercules Films is deciding on the price of the video release of its film Bride of Frankenstein. The marketing department estimates that at a selling price of p dollars it can sell q = 300000 - 8000 p copies.
Each copy cost $4 to make.
What price p will give the greatest profit? (SHOW WORK)
2.)The U.S. Postal Service (USPS) will accept packages only if the length plus girth is no more than 118 inches.
Assuming that the front face of the package is square, what is the width of the package that the USPS will accept that has the Maximum Volume? (SHOW WORK)
3.)FeatureRich Software Company has a dilemma. Its new program Doors-12.0, is almost ready to go on the market. However, the longer the company works on it, the better is can make the program and the more it can charge for it. The company's marketing analysts estimate that if it delays t days, it can set the price at p = 98 +2t dollars. On the other hand, the longer it delays, the more market they will lose to their main competitor so that if it delays t days it will be able to sell 360000 - 2800t copies of the program. How many days should FeatureRich delay the release in order to get the greatest revenue? (SHOW WORK)
4.)One farmer is planting a fruit orchard. He has 580 meters of fencing to use. He wants to separate
Explanation / Answer
1.)
p = (300000- q)/8000
Total revenue = p*q = (300000*q- q^2)/8000
Marginal revenue = derivatie of Total revenue w.r.t q = d(TR)/dq
MR = d(TR)/dq = (300000 - 2q)/8000
Marginal cost = Each copy cost = $4
MC = $ 4
So at Max. Profit
MR = MC
(300000 - 2q)/8000 = 4
300000 - 2q = 32000
q = (300000 - 32000)/2 = 134,000
p = (300000- q)/8000
p = $ 20.75
2) suppose
Length = l
Side of Square = s
l + 4*s = 118
l = 118 - 4s
and
V = l*b*h = l*s*s = l*s^2 = s^2*(118-4s) = 118s^2 - 4s^3
dV/ds = 0 for maxima
dV/ds = 2*118*s - 12*s^2 = 0
so 2*118 - 12*s = 0
s = (2*118)/12 = 19.667 inches
ans = 19.667 inches
3)
Revenue = Price* quantity = (98+2t) * ( 360000 - 2800*t)
dR/dt = 0
dR/dt = 2*( 360000 - 2800*t) - 2800*(98+2t) = 0
2*( 360000 - 2800*t) = 2800*(98+2t)
(360000 - 2800t) = 1400*98 + 2800t
222800 = 5600*t
t = 39.785 days
4)
Perimeter = (3x*2 + 3*y) = 6x + 3y = 580
Dividing by 3
2x+y = 580/3
y = (580/3 - 2x)
Area = x*y + 2x*y = 3xy = 3x*(580/3 - 2x) = (580*x - 6x^2)
dA/dx = 0 for maxima
580 - 12x = 0
x = 48.3333 m
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