S1 = x
s2 = 2x
s3 = 3x - 3
51 = s1 + s2 + s3
51 = x + 2x + 3x - 3
54 = 6x
9 = x
The length of the first side is 9
Answer:
- r = 12.5p(32 -p)
- $16 per ticket
- $3200 maximum revenue
Step-by-step explanation:
The number of tickets sold (q) at some price p is apparently ...
q = 150 + 25(20 -p)/2 = 150 +250 -12.5p
q = 12.5(32 -p)
The revenue is the product of the price and the number of tickets sold:
r = pq
r = 12.5p(32 -p) . . . . revenue equation
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The maximum of revenue will be on the line of symmetry of this quadratic function, which is halfway between the zeros at p=0 and p=32. Revenue will be maximized when ...
p = (0 +32)/2 = 16
The theater should charge $16 per ticket.
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Maximum revenue will be found by using the above revenue function with p=16.
r = 12.5(16)(32 -16) = $3200 . . . . maximum revenue
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<em>Additional comment</em>
The number of tickets sold at $16 will be ...
q = 12.5(32 -16) = 200
It might also be noted that if there are variable costs involved, maximum revenue may not correspond to maximum profit.
Split up the integration interval into 4 subintervals:
The left and right endpoints of the -th subinterval, respectively, are
for , and the respective midpoints are
We approximate the (signed) area under the curve over each subinterval by
so that
We approximate the area for each subinterval by
so that
We first interpolate the integrand over each subinterval by a quadratic polynomial , where
so that
It so happens that the integral of reduces nicely to the form you're probably more familiar with,
Then the integral is approximately
Compare these to the actual value of the integral, 3. I've included plots of the approximations below.
For #1:
look at the chart and write the percentages that are by the name of the food and write the percentages next to the names
For #2:
take the percentage number and divide it by 2 (because it was 50 customers out of 100%) for example if 50% of the customers picked apples then divide it by 2 and 25 customers would have gotten apples and put that number next to the name
Hope that helps :D