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20 May, 16:14

A company distributes college logo sweatshirts and sells them for $55 each. The total cost function is linear, and the total cost for 50 sweatshirts is $4346, whereas the total cost for 240 sweatshirts is $7576. (a) Write the equation for the revenue function R (x).

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  1. 20 May, 17:11
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    The revenue equation is TR=55*P

    Total cost equation is TC=3496+17Q

    Explanation:

    The formula for revenue is given quantity multiplied by price

    TR=PQ

    P is the price per unit ]

    Q is the total quantity

    since P is $55

    TR=55P

    The total cost function can also be determined thus:

    TC = a+bQ

    where a is the fixed cost

    b is variable cost per unit

    Q is the number of output

    when TC is $4346, Q was 50

    when TC was $7576 Q was 240

    7576=a+240b

    4346=a+50b

    subtracting the two equations

    3230 = 190b

    b=3230/190

    b=$17

    by substituting b in any of the equations, fixed cost can be determined

    4346=a + (17*50)

    4346=a+850

    a=4346-850

    a=3496

    Total cost function

    TC=3496+17Q
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