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5 March, 02:54

A company distributes college logo sweatshirts and sells them for $50 each. The total cost function is linear, and the total cost for 90 sweatshirts is $3564, whereas the total cost for 260 sweatshirts is $5944. (a) Write the equation for the revenue function R (x)

(b) Write the equation for the total cost function

(c) Find the break-even quantity. sweatshirts

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  1. 5 March, 04:43
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    The total revenue equation is TR=50Q

    The total cost equation TC=2304+14Q

    Equilibrium quantity is 64

    Step-by-step explanation:

    The total cost function can be written TC=a+bQ, where TC is the total cost, a fixed cost, b is the variable cost per unit and Q the quantity produced

    Revenue function can be given TR=P*Q, where TR is total revenue, P is the price per unit and Q quantity sold

    since P is $50

    TR=50P

    when TC=$3564,

    3564=a+90Q equation 1

    when TC=$5944

    5944=a+260bequation 2

    Solving simultaneously, we subtract equation 1 from 2

    5944=a+260b

    3564=a+90b

    2380=170b

    b=2380/170

    b=$14

    We substitute for b in any of the equations

    3564=a + (14*90)

    3564=a+1260

    a=3564-1260

    a=2304

    Hence the total cost equation is

    TC=2304+14Q

    At equilibrium TC = TR

    50P=2304+14Q

    50P-14Q=2304

    36Q=2304

    Q=64
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