<span>cost of producing x radios is c(x) = 400 + 20x - 0.2x
where:
x=number of units
thus the cost required to produce 30 units will be given by
c(30)=400+20(30)-0.2(30)
c(30)=400+600-6
c(30)=994
Answer: Marginal cost will be $994</span>
You do the distance times by the amount of time
We can simplify the expression with patience and a little mathematical tinkering.
The simplified expression is shown in the attached picture, along with more information obtained about your expression.
The objective is to add similar terms and fractions and group them together to form a solution in a compact, elegant form.
Let the square base of the container be of side s inches and the height of the container be h inches, then
Surface are of the container, A = s^2 + 4sh
For minimum surface area, dA / ds + dA / dh = 0
i.e. 2s + 4h + 4s = 0
6s + 4h = 0
s = -2/3 h
But, volume of container = 62.5 in cubed
i.e. s^2 x h = 62.5
(-2/3 h)^2 x h = 62.5
4/9 h^2 x h = 62.5
4/9 h^3 = 62.5
h^3 = 62.5 x 9/4 = 140.625
h = cube root of (140.625) = 5.2 inches
s = 2/3 h = 3.47
Therefore, the dimensions of the square base of the container is 3.47 inches and the height is 5.2 inches.
The minimum surface area = s^2 + 4sh = (3.47)^2 + 4(3.47)(5.2) = 12.02 + 72.11 = 84.13 square inches.
