The total revenue and total cost functions for manufacturing Items are:

TR (q) = -5q2+80q and TC (q) = q3-12q2+60q+60,

where q is measured in hundreds of Items and total revenue and total cost are given in hundreds of dollars.

(a) Determine the quantity at which marginal revenue is 62 dollars per Thing.

1.8 hundred or 180 Items

Explanation:

Total Revenue is the total value of goods & services sold.

TR = Price x Quantity

Total Revenue = 80q - 5q^2

Marginal Revenue is the change in Total Revenue, when an additional unit is sold.

MR = ΔTR / ΔQ

= d (80q - 5q^2) / dq

MR = 80 - 10q

To find : Quantity 'q' at which Marginal Revenue (MR) = 62

So, 80 - 10q = 62

80 - 62 = 10q

18 = 10q

q = 18 / 10

= 1.8 hundred items

= 180 items