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Profit and loss

This topic has 5 expert replies and 0 member replies
vaibhav101 Senior | Next Rank: 100 Posts Default Avatar
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Profit and loss

Post Mon Jun 05, 2017 5:04 am
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 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

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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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GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
Followed by:
113 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Most Active Expert Most Responsive Expert Most Thanked 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

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Thanked by: vaibhav101
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
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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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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