ACME’s manufacturing costs for sets of horseshoes

Here's a slight twist:

It COSTS $19.75 per set, and each set is SOLD for $52.50
So, the company makes approximately $33 per set ($52.50 - $19.75 ≈ $33)

The company sold 987 sets.
So, the profit ≈ ($33)(1000) ≈$33,000

Keep in mind, that there's also the initial outlay of $11,450

So, the TOTAL PROFIT ≈$33,000 - $11,450
≈ $21,500

The best (closest) answer is A

Cheers,
Brent

The alternative choices ARE far apart (except the last two ones), therefore we are allowed to use (always carefully!) approximations (to be reconsidered ONLY if we come close to $50,000) !!

\(? = {\rm{revenue}} - {\rm{costs}}\,\,\,\,\,\,\left( {{\rm{987}}\,\,{\rm{sets}}} \right)\)

\({\rm{revenue}} = 987\,\,sets\,\,\left( {{{\$ 52{1 \over 2}} \over {1\,\,{\rm{set}}}}} \right)\,\,\,\, \cong \,\,\,\$ 990 \cdot 52\)

\({\rm{costs}}\,\,\,{\rm{ = }}\,\,\,{\rm{11450 + }}987\,\,sets\,\,\left( {{{\$ 19{3 \over 4}} \over {1\,\,{\rm{set}}}}} \right)\,\,\,\, \cong \,\,\,\$ \left( {11450 + 990 \cdot 20} \right)\)

\(? \cong \,10 \cdot 99 \cdot \left( {52 - 20} \right) - 11450 \cong 10 \cdot 100 \cdot 32 - 11450 \cong 21000\,\,\left( \$ \right)\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.

The profit is:

987(52.50) - [11,450 + 987(19.75)]

987(52.50) - 11,450 - 987(19.75)

987(52.50 - 19.75) - 11,450

987(32.75) - 11,450

At this point, we will approximate 987 as 1,000 and 32.75 as 32. So the approximate total profit is:

1,000(32) - 11,450

32,000 - 11,450

20,550

We see that this is closest to 20,874.25 in choice A.

Alternate Solution:

Let’s round all the numbers. From the final statement of the problem, we know we’ll sell about 1,000 sets. The initial outlay is about 12,000 and manufacturing costs are about (20) (1000) = 20,000. Thus, costs are about 32,000. Revenue is a bit greater than (50)(1000) = 50,000. Thus, revenue - cost = 50,000 - 32,000 = 18,000. Thus, profit is a bit greater than $18,000.

Answer: A