To fund your dream vacation, you plan to save $1,475 per year for the next 15 years starting one year from now. If you can earn
1 answer:
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Answer:
$10.67
Explanation:
Data provided in the question:
Initial cost = $3
Initial selling cost = $5
Initial sales = 4000
with $1 increase in price she loses 300 sales per month
Now,
Let the increase in price which maximizes the profit be '$x'
Therefore,
Final selling price = $5 + x
Final sales = 4000 - 300x
Thus,
Revenue = Final selling price × Final sales
= ( 5 + x)( 4000 - 300x)
= 20,000 - 1500x + 4000x - 300x²
= 20,000 + 2500x - 300x²
Total Cost = Initial cost × Final sales
= 3(4000 - 300x )
= 12,000 - 900x
Now,
Profit = Total revenue - Total cost
or
P = [ 20,000 + 2500x - 300x² ] - [ 12,000 - 900x ]
or
P = 8,000 + 3400x - 300x²
for point of maxima
Thus,
0 = 0 + 3400 - 300(2x)
or
0 = 3400 - 600x
or
600x = 3400
or
x =
Hence,
The price will be = $5 + x =
= $10.67