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28 August, 09:00

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.

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  1. 28 August, 12:28
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    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
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