Nelly runs a 10 mile race in 88 minutes. At this rate, how long would it take him to run a 6.5 mile race?
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It is a bit tedious to write 6 equations, but it is a straightforward process to substitute the given point values into the form provided.
For segment ab. (x1, y1) = (1, 1); (x2, y2) = (3, 4).
... x = 1 + t(3-1)
... y = 1 + t(4-1)
ab = {x=1+2t, y=1+3t}
For segment bc. (x1, y1) = (3, 4); (x2, y2) = (1, 7).
... x = 3 + t(1-3)
... y = 4 + t(7-4)
bc = {x=3-2t, y=4+3t}
For segment ca. (x1, y1) = (1, 7); (x2, y2) = (1, 1).
... x = 1 + t(1-1)
... y = 7 + t(1-7)
ca = {x=1, y=7-6t}
Given that for each <span>$2 increase in price, the demand is less and 4 fewer cars are rented.
Let x be the number of $2 increases in price, then the revenue from renting cars is given by
.
Also, given that f</span><span>or each car that is rented, there are routine maintenance costs of $5 per day, then the total cost of renting cars is given by
Profit is given by revenue - cost.
Thus, the profit from renting cars is given by
</span><span>
For maximum profit, the differentiation of the profit function equals zero.
i.e.
</span><span>
The price of renting a car is given by 48 + 2x = 48 + 2(8) = 48 + 16 = 64.
Therefore, the </span><span>rental charge will maximize profit is $64.</span>
Let x be the number of $2 increases in price, then the revenue from renting cars is given by
Also, given that f</span><span>or each car that is rented, there are routine maintenance costs of $5 per day, then the total cost of renting cars is given by
Profit is given by revenue - cost.
Thus, the profit from renting cars is given by
</span><span>
For maximum profit, the differentiation of the profit function equals zero.
i.e.
</span><span>
The price of renting a car is given by 48 + 2x = 48 + 2(8) = 48 + 16 = 64.
Therefore, the </span><span>rental charge will maximize profit is $64.</span>