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Profit and loss

This topic has 5 expert replies and 0 member replies

Profit and loss

Post Mon Jun 05, 2017 5:04 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    The manufacturer of a certain item can sell all he can produce at the selling price of $60 each. It costs him $40 in materials and labour to produce each item and he has overhead expenses of $3000 per week in order to operate the plant. The minimum number of units that he should produce and sell in order to make profit of at least $1000 per week, is
    A 200
    B 250
    C 300
    D 400
    E 500

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    Post Mon Jun 05, 2017 5:12 am
    vaibhav101 wrote:
    The manufacturer of a certain item can sell all he can produce at the selling price of $60 each. It costs him $40 in materials and labour to produce each item and he has overhead expenses of $3000 per week in order to operate the plant. The minimum number of units that he should produce and sell in order to make profit of at least $1000 per week, is
    A 200
    B 250
    C 300
    D 400
    E 500
    Let x = the number of units produced in 1 week.

    It costs him $40 in materials and labour to produce each item and he has overhead expenses of $3000 per week in order to operate the plant.
    TOTAL EXPENSES for 1 week = 40x + 3000

    The manufacturer of a certain item can sell all he can produce at the selling price of $60 each.
    So, the manufacturer will sell x units at $60 apiece
    TOTAL REVENUE for 1 week = 60x

    PROFIT = 60x - ( 40x + 3000)
    = 20x - 3000

    The minimum number of units that he should produce and sell in order to make profit of at least $1000 per week, is
    We can write the equation: 20x - 3000 = 1000
    Add 3000 to both sides: 20x = 4000
    Solve: x = 200

    Answer: A

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    Post Mon Jun 05, 2017 10:22 am
    Hi vaibhav101,

    This question can be solved by TESTing THE ANSWERS.

    We're told that each unit costs $40 to produce and will be sold for $60. In addition, the production plant costs $3,000 per week to operate. We're asked for the minimum number of units that must be produced in one week to net at least a $1,000 profit.

    Let's TEST Answer B: 250 units

    250 units would net $20/profit each...
    (250)($20) = $5,000
    After subtracting the $3,000 needed to run the plant, we have...
    $5,000 - $3,000 = $2,000
    This is higher than what we were asked for, so 250 units is clearly too many to produce the minimum profit we were after. There's only one answer left that 'fits'

    Final Answer: A

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    Post Mon Jun 05, 2017 9:15 pm
    vaibhav101 wrote:
    The manufacturer of a certain item can sell all he can produce at the selling price of $60 each. It costs him $40 in materials and labour to produce each item and he has overhead expenses of $3000 per week in order to operate the plant. The minimum number of units that he should produce and sell in order to make profit of at least $1000 per week, is
    A 200
    B 250
    C 300
    D 400
    E 500
    We see that at $60 selling price and $40 cost price, there is a margin of $20 per unit. If there are x units to be produced, they must bring in the total margin (20x) that can at least cover overhead expense ($3000) and profit ($1000).

    Thus, 20x ≥ (3000 + 1000) => 20x ≥ 4000 => x ≥ 200 units.

    The correct answer: A

    Hope this helps!

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    GMAT/MBA Expert

    Post Mon Jun 05, 2017 11:39 pm
    Costs: $40 per item + $3000
    Profits: $60 per item

    If our guy sells x items and makes $1000, we know that

    Profits - Costs = $1000

    60x - (40x + 3000) = 1000

    20x - 3000 = 1000

    20x = 4000

    x = 200

    Thanked by: vaibhav101
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    Post Sat Jun 10, 2017 7:41 am
    vaibhav101 wrote:
    The manufacturer of a certain item can sell all he can produce at the selling price of $60 each. It costs him $40 in materials and labour to produce each item and he has overhead expenses of $3000 per week in order to operate the plant. The minimum number of units that he should produce and sell in order to make profit of at least $1000 per week, is
    A 200
    B 250
    C 300
    D 400
    E 500
    We can let x = the number of items sold.

    Thus, the revenue from selling x items is 60x.

    The cost of producing x items is 40x and there is a fixed cost of $3,000. Thus, the total cost is 40x + 3000.

    Since revenue - cost = profit and we want the profit to be at least $1,000, we can now determine the minimum value of x using the following inequality:

    60x - (40x + 3,000) ≥ 1000

    60x - 40x - 3,000 ≥ 1000

    20x - 3,000 ≥ 1000

    20x ≥ 4000

    x ≥ 200

    Answer: A

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