What stands for "the per-person rate"?
What stands for "the number of riders"?
What is their product?
Then differentiate, and maximize. (You will end up with a negative quadratic function, which you learned about back in algebra. From what you learned about graphing back then, you know that there is exactly one max/min point, being the vertex, and that, for a negative quadratic, the vertex is the maximum.)
For what does the N-value stand?
Differentiate, set equal to zero, and maximize. (Since the function is an upside-down quadratic, you know, from back in algebra, that the only critical point will of course be the vertex, and will be the maximum.)
At the maximum, what does "t" represent?
At the maximum, what does "N" represent?
On the upper line, to the right of B, label a point as C; label the distance between B and C as 300.
The "nearest telephone station" is at A; the cottage is at C.
Draw a slanty line from A to some point D between B and C. This is the optimal path that you need to find. Label BD as x.
What then is (the expression for) the value of DC?
ABD is a right triangle with legs having lengths 120 and x. What then is (the expression for) the length of AD?
You are given that the cost, along the slanty line AD, is $15 per meter. What then is (the expression for) the cost of AD?
You are given that the cost, along DC, is $10 per meters. What then is (the expression for) the cost of DC?
What then is the expression for the total cost?
Find the value of x that minimizes this cost.
If you get stuck, please reply showing how far you have gotten in working through the steps. Thank you!