Math help?

General
1

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.

2

Not done maths in a while here, got a scrap piece of paper and did some trial and error for q2. My rectangle came out to be 416ft in length (x3 being its split in half) and 208 in width.

416 x 3 add 208 x 2 gives you 1644ft of fence used. I have no idea how to work out area or anything… I do probably just forgot. For working out I did trial and error until i got 1644.

I will try and do more, even thought it’ll be wrong aahhaha

please humiliate me if I’m wrong :smile:

q3

The side parallel to the barn should be 24 feet long and the other two sides should be 12 feet long each.

Once again I did trial and error can’t really explain how i got it

3

Not sure if you still need these but here is the first.

  1. P = 36-6Q
    Revenue® = P*Q (Solve for R in terms of P)
    R = 36-6Q^2 (Find maximum using graphing utility)
    Maximum revenue is $54 when units sold is 3 and price per unit is $18

These optimization problems are all generally the same. Most of the time you need to substitute and stuff until you get a parabola and find the maximum on the graph.