A company produces and sells 211,600 boxes of t-shirts each year. Each production run has a fixed cost of $400 and an additional cost of $3

Question

A company produces and sells 211,600 boxes of t-shirts each year. Each production run has a fixed cost of $400 and an additional cost of $3 per box of t-shirts. To store a box for a full year costs $2. What is the optimal number of production runs the company should make each year? Do not include units with your answer.

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Amelia 2 weeks 2021-10-10T20:37:49+00:00 1 Answer 0

Answers ( )

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    2021-10-10T20:39:25+00:00

    Answer:x=46

    Step-by-step explanation:

    Given

    Company Produces and sells 211600 boxes of T-shirt each year

    Fixed cost =$ 400

    Additional cost = $ 3 per box

    storage cost =$ 2

    let x be the no of production run

    therefore

    Holding cost per year =holding\ cost\times average\ holding\ items=2\times \frac{211600}{2x}=\frac{211600}{x}

    Yearly\ ordering\ cost=cost\ during\ each\ order\times number\ of\ order\ Placed\ per\ year

    yearly ordering cost=400x+3\times \frac{211600}{x}

    Total cost C(x)=\frac{211600}{x}+400x+3\times \frac{211600}{x}

    differentiate C(x) w.r.t to x we get

    \frac{\mathrm{d} C(x)}{\mathrm{d} x}=400-\frac{3\times 211600}{x^2}-\frac{1}{211600}

    Put \frac{\mathrm{d} C(x)}{\mathrm{d} x}=0 to get max/min value

    400-\frac{211600}{x^2}-\frac{3\times 211600}{x^2}=0

    x^2=\frac{211600}{100}

    x=\sqrt{2116}

    x=46

    therefore 46 runs must be performed

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