Wednesday, September 22, 2010

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.





Essentially, what we are given in the question is:
Gross Profit = 1000(k+60)-1000k + t
With 1), we can get the revenue portion and find "k":
1000k+60,000=150,000
1000K = 90,000
K= 90
So what we have in the overall equation is: 1000(90+60) - 1000(90)+t. We don't have "t" so this is INSUFFICIENT.
With 2), we can get the cost side:
500k+t=1000K+t-45000
Notice the "t" cancels out. We are left with:
500K=1000K-45000
500K=45000
K=90
Again, we only get K=90. So with 2), we still only have:1000(90+60) - 1000(90)+t. INSUFFICIENT
Unless we have "t" we don't know what the gross profit is. So even with 1) and 2) together, we can't solve for "t." Therefore, E is the correct answer


ans: E

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