For manufacturer M, the cost C of producing X units of its product per month is given by c=kx+t, where c is in dollars and k and t are constants. Last month, if manufacturer M produced 1000 units of its product and sold all the units for k+60 dollars each, what was manufacturer M's gross profit on the 1000 units?
1) Last month, manufacturer M's revenue from sale of the 1000 units was $150,000
2) manufacturer M's cost of producing 500 units in a month is $45000 less than its cost of producing 1000 units in a month.
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- shashank.ism
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c=kx+tabhasjha wrote:For manufacturer M, the cost C of producing X units of its product per month is given by c=kx+t, where c is in dollars and k and t are constants. Last month, if manufacturer M produced 1000 units of its product and sold all the units for k+60 dollars each, what was manufacturer M's gross profit on the 1000 units?
1) Last month, manufacturer M's revenue from sale of the 1000 units was $150,000
2) manufacturer M's cost of producing 500 units in a month is $45000 less than its cost of producing 1000 units in a month.
last month C= 1000k+t
S= K+60
P=S-C= (K+60)*1000 -1000k +t
statement 1: P=150000
so (K+60)*1000 - 1000k+t = 15000 --->t=-45000.....but k can't be calculated.....not sufficient
statement 2: C500 = 500k+t c1000 = 1000k+t
--> 500k+t +45000 = 1000k+t --> k = 90 but t can't be calculated not sufficient
combined: both k and t known..
so profit can be calculated
Hence ans is
C
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- ajith
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cost producing 1000 units = 1000k+tabhasjha wrote:For manufacturer M, the cost C of producing X units of its product per month is given by c=kx+t, where c is in dollars and k and t are constants. Last month, if manufacturer M produced 1000 units of its product and sold all the units for k+60 dollars each, what was manufacturer M's gross profit on the 1000 units?
1) Last month, manufacturer M's revenue from sale of the 1000 units was $150,000
2) manufacturer M's cost of producing 500 units in a month is $45000 less than its cost of producing 1000 units in a month.
Revenue = (k+60)*1000
Gross profit = 60000-t
1.) revenue = 150,000 => k = 90 Doesnt help to calculate profit
2) Cost of producing 500 units = 500k+t
Cost of producing 1000 units = 1000k +t
500k = 45000
k = 90
Insufficient to calculate t
1&2 combined also is insufficient to calculate t
Hence E
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I'm a little confused on this..
the revenue = 1000(K+60) - (1000K + t) = 60,000 - T. So we need T to solve
S1 - gives us K ..still not T
S2 - 500 units cost 45K less than 1000, therfefore can I assume 500 units cost 45K to manufacture? Based on this
45000 = 500K + T..
I derived K from S1, substitute for K to derive T. Answer C
What's wrong with this approach???
Thanks
nix
the revenue = 1000(K+60) - (1000K + t) = 60,000 - T. So we need T to solve
S1 - gives us K ..still not T
S2 - 500 units cost 45K less than 1000, therfefore can I assume 500 units cost 45K to manufacture? Based on this
45000 = 500K + T..
I derived K from S1, substitute for K to derive T. Answer C
What's wrong with this approach???
Thanks
nix
- ajith
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That is where it goes wrongNIXBTG wrote: S2 - 500 units cost 45K less than 1000, therfefore can I assume 500 units cost 45K to manufacture? Based on this
45000 = 500K + T..
the equation 45000 = 500K + T is wrong
Instead it should have been 45000 = 500K
manufacturer M's cost of producing 500 units in a month is $45000 less than its cost of producing 1000 units in a month
Cost of producing 500 units = 500K+T
Cost of producing 1000 units = 1000K +T
The difference = 500K (and not 500K +T) = 45000
Hope it is clear
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- Anaira Mitch
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c=kx+t
In last month, cost=1000k+t; profit=1000(k+60) -(1000k+t) =60000-t, so, we need to solve t.
From 1, 150000=1000*(k+60), there is no information about t.
From 2, (1000k+t)-(500k+t)=45000, still cannot solve out t.
Answer is E
In last month, cost=1000k+t; profit=1000(k+60) -(1000k+t) =60000-t, so, we need to solve t.
From 1, 150000=1000*(k+60), there is no information about t.
From 2, (1000k+t)-(500k+t)=45000, still cannot solve out t.
Answer is E
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- Jay@ManhattanReview
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Given that c = kx+tabhasjha wrote:For manufacturer M, the cost C of producing X units of its product per month is given by c=kx+t, where c is in dollars and k and t are constants. Last month, if manufacturer M produced 1000 units of its product and sold all the units for k+60 dollars each, what was manufacturer M's gross profit on the 1000 units?
1) Last month, manufacturer M's revenue from sale of 1000 units was $150,000
2) manufacturer M's cost of producing 500 units in a month is $45000 less than its cost of producing 1000 units in a month.
Revenue from the sale of 1000 units = 1000*(k+60) = 1000k+60,000
Cost of 1000 units = 1000k+t
Thus, Gross profit from the sale of 1000 units = (1000k+60,000) - (1000k+t) = 60,000-t
So, the rephrased question is: What is the value of t?
It is important to note that whether we get/do not get the value of k, it would have no impact on the question.
S1: Last month, manufacturer M's revenue from the sale of 1000 units was $150,000.
Revenue from the sale of 1000 units = 1000k+60,000 = 150,000 => k = 90. We do not have the value of t. Insufficient.
S2: Manufacturer M's cost of producing 500 units in a month is $45000 less than its cost of producing 1000 units in a month.
Difference of 'cost of producing 1000 units' and 'cost of producing 500 units' = (1000k+t) - (500k+t) = 500k = 45,000 => k =90. We do not have the value of t. Insufficient.
S1 and S2:
Even after combining both the statements, we cannot get the value t.
Answer: E
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This is an excellent way of solving: very concise, and clearly stating (and searching for) the required missing piece. Absolutely the way to go!Anaira Mitch wrote:c=kx+t
In last month, cost=1000k+t; profit=1000(k+60) -(1000k+t) =60000-t, so, we need to solve t.
From 1, 150000=1000*(k+60), there is no information about t.
From 2, (1000k+t)-(500k+t)=45000, still cannot solve out t.
Answer is E
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For manufacturer M, the cost c of producing x units of its product per month is given by c=kx+t, where c is in dollars and k and t are constants. Last month, if manufacturer M produced 1000 units of its product and sold all the units for k+60 dollars each, what was manufacturer M's gross profit on the 1000 units?abhasjha wrote:For manufacturer M, the cost C of producing X units of its product per month is given by c=kx+t, where c is in dollars and k and t are constants. Last month, if manufacturer M produced 1000 units of its product and sold all the units for k+60 dollars each, what was manufacturer M's gross profit on the 1000 units?
1) Last month, manufacturer M's revenue from sale of the 1000 units was $150,000
2) manufacturer M's cost of producing 500 units in a month is $45000 less than its cost of producing 1000 units in a month.
1) Last month, manufacturer M's revenue from sale of the 1000 units was $150,000.
2) manufacturer M's cost of producing 500 units in a month is $45000 less than its cost of producing 1000 units in a month.
We are given the formula c = kx + t, in which c is in dollars, x is the number of units produced per month, and k and t are constants. We are also given that last month manufacturer M produced 1000 units of its product and sold all the units for k + 60 dollars each. We need to determine manufacturer M's gross profit on the 1000 units. Thus, we have:
c = k(1,000) + t
Furthermore, since the manufacturer sells 1000 units for k + 60 dollars each, its revenue was 1000(k + 60) = 1000k + 60000. So, the gross profit is 1000k + 60000 - (1000k + t ) = 60000 - t. As we can see, if we can determine the value of t, then we can answer the question.
Statement One Alone:
Last month, manufacturer M's revenue from sale of the 1000 units was $150,000.
Using the information in statement one, we can create the following equation:
1000k + 60,000 = 150,000
1000k = 90,000
k = 90
Although we have a value for k, we have no information about the value of t. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
Manufacturer M's cost of producing 500 units in a month is $45,000 less than its cost of producing 1000 units in a month.
Using the information in statement two, we can create the following equation:
k(1,000) + t - [k(500) + t] = 45,000
1,000k + t - 500k - t = 45,000
500k = 45,000
k = 90
Although we have a value for k, we still do not have enough information to determine the value of t. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:
Since each statement allows us to find only the value of k (recall k = 90 in each statement), we still do not have enough information to determine the value of t, so we cannot determine the profit last month.
Answer: E
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