I have a few problems for math that I cannot solve for my life, and my professor will not help me even if I am stuck and can’t continue. If you guys could help me solve these few problems and show some work maybe so I can understand how you got the answer that would be great (rather than just give me the answer)

I will love you forever!

1: The demand function for a product is p=36−6q where p is the price in dollars when q units are demanded. Find the level of production that maximizes the total revenue and determine the revenue. q=____ R$=____ R is the revenue (total I think)

2: A farmer wants to fence a rectangular field and then divide it in half with a fence down the middle parallel to one side. If 1644 ft of fence is to be used, what is the maximum area of the lot that he can obtain? A =_____ square feet.

3: A farmer wants to fence a small rectangular yard next to a barn. Fence for side parallel to the barn will cost 50 per foot and the fence for the other two sides will cost 20 per foot. The farmer has a total of 1700 dollars to spend on the project. Find the dimensions for the yard that will have the largest possible area.

The side parallel to the barn should be __________ feet long and the other two sides should be _______ feet long each.

4: Suppose that each day a company has fixed costs of 400 dollars and variable costs of 0.7x+1450 dollars per unit, where x is the number of units produced that day. Suppose further that the selling price of its product is 1500−0.25x dollars per unit.

(a) Each day, the company breaks even at production levels ________ units.

(Enter your answers as a comma-separated list, if necessary)

(b) The maximum daily revenue attained is ________ dollars.

© The price that maximizes profit is ________ dollars per unit.