need help with min/max word problems plz, someone help, i dont get this at all

my teacher is giving these word problems, and i am not getting them, the problems is not solving them, problem is the let statements, how to create them, what keywords to look for, and how to create an equation essentially solving is no problem plz help, test on friday,

some example of questions are

a farmer wants a rectangular field with 180m of fenching, what are the dimensions of the field if the area is to be a maximum?

Tow numbers have a sum of 36, find the number if the sum of theri squares is a minumium and state the minimum

a theathre group presently charges $12 to see a play, for each 2$ increase in the ticket price, the group figures it will lose 100 pators, the theathre can hold 1200 people,

what is the maximum possible revenue, what ticket price produces the maximum, how many patrons are neeed to provide this maximum revenue.

Assume that a jogger burns callories at a rate given by B= -3/2v^2 + 48v +561 for 0< v <30

B is calories burned per hour and v is the joggers speeed in km/h

what is the maxmimum number of calories that can be burned per hour?, at what speeed is the maximum achieved.

THERE are alot more, but help with these will be greatly appreciated. ty

yea i understand what u mean

problem is my teacher just came out of retirement so he cant explain it to me properly, and my class is advanced functions grade 11, not at calc yet anyways thx for help