Find the unit price that will maximize the total revenue?

Question

When priced at $40.00 each, a toy has annual sales of 5,000 units. The manufacturer estimates that each $1.00 increase in cost will decrease sales by 100 units. Find the unit price that will maximize the total revenue

Answer 1

$45*4500= $202,500

Answer 2

properly once you look at it for the 2d, it says there are 1000 tickets bought and it fills the theater 80%. subsequently, one hundred% skill is 1200 persons. so as that means we've 200 quantities we ought to study to discover earnings maximization. (I lamentably don't have a calculator available) you will ought to graph the function, you gets a curve. discover the max on the curve, wherein the marginal earnings is same to 0 and additionally you have have been given your self the component of earnings maximization. (i visit objective to discover a calculator and be conscious if i will do this myself). the guy or woman below is mistaken. one hundred% skill does now no longer verify earnings maximization. you ought to graph this and discover a element on the curve wherein marginal earnings = 0.

Answer 3

original no of units=5000
original price=$40
original revenue=5000*40
if the price is increased by n dollars
sale=5000-100n
revenue=(5000-100n)(40+n)
=200000-100n^2-4000n+5000n
=-100n^2+1000n+200000
dR/dn=-200n+1000
setting it to zero for R max
200n=1000
n=1000/200=5
so the revenue will be maximum
at 45 dollars price and the revenue
=45*4500
=$202500

Answer 4

increase in price of x. new price = 40 + x
units sold will decrease by 100x. new total units sold = 5000-100x
total revenue = f(x) = (5000 - 100x)(x + 40)
to find local maxima find f'(0)

Answer 5

u = 5,000 - 100(p - 40)
R = u*p = 5000p - 100p^2 + 4000p
R = 9,000p -100p^2 = p(9,000 - 100p)
dR/dp = 9,000 - 200p = 0
p = 9,000/200 = $45
u = 5,000 - 4,500 + 4,000
u = 4,500
R = $202,500

Check:
R = 44(9,000 - 100*44) = $202,400 < $202,500
R = 46(9,000 - 100*46) = $202,400 < $202,500