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2 August, 01:46

Minden Company introduced a new product last year for which it is trying to find an optimal selling price. Marketing studies suggest that the company can increase sales by 5,000 units for each $2 reduction in the selling price. The company's present selling price is $70 per unit, and variable expenses are $40 per unit. Fixed expenses are $540,000 per year. The present annual sales volume (at the $70 selling price) is 15,000 units. Assuming that the marketing studies are correct, what is the maximum annual profit that the company can earn? At how many units and at what selling price per unit would the company generate this profit?

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  1. 2 August, 03:50
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    P = 38

    Q = 95,000

    max profit: 2,310,000

    Explanation:

    cost: 540,000 + 40Q

    marginal cost: dC/dQ = 40

    based on the current price and sales and the marketing studies we build for the inverse demand function:

    Q = aP + b

    if P = 70 then, Q = 15,000

    if P = 68 then, Q = 20,000

    -2P = + 5,000Q

    -1P then, 2,500 Q

    15,000 = - 2,500 (70) + b

    b = 190,000

    so Q = - 2,500P + 190,000

    revenue; P x Q

    P x (-2,500P + 190,000)

    -2,500P2 + 190,000P

    marginal revenue: dR/dQ = - 5,000P + 190,000

    max profit at MR = MC

    40 = 190,000 - 5,000P

    189,960 / 5,000 = 37.992‬ = 38

    Q = - 2,500 (38) + 190,000 = 95,000

    Profit:

    (70 - 40) 95,000 - 540,000 = 2,850,000 - 540,000 = 2,310,000
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