For manufacturer M, the cost C...

[steph]

DS prob: 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.

ans: E

I am keep getting C :-( i might be using a wrong formula. Revenue = Gross profit - Expense. right? is there other relevant formulas for this prob?
thanks so much in advance.

Steph

[mbandai]

I think it's Gross Profit = Revenue- Cost.

Notice that when you work the two conditions out, they essentially give you a value to one unknown variable, "k", but not "t." We would need to know what "t" is to be able to calculate the gross profit.

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

[RonPurewal]

mbandai: nicely done.