Problem Solving

AAPL wrote:ACME's manufacturing costs for sets of horseshoes include at $11,450 initial outlay, and $19,75 per set. They can sell the sets $52.50. If profit is revenue from sales minus manufacturing costs, and the company produces & sales 987 sets of horseshoes, what was their profit?

A. $20,874.25
B. $30,943.25
C. $41,308.50
D. $51,817.50
E. $53,624.25

The OA is A.

I solved this PS question as follows,

Approximations
19.75 = 20.00
52.50 = 50.00
987 = 1000

Initial cost = 20*1000 + 11450 = 31450
Selling = 50 * 1000 = 50000
Profit = 50000 - 31450 = 19000, close to 20000 Option A.

Has anyone another approach to solve this PS question? Regards!

That's a great solution.
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

AAPL wrote:ACME's manufacturing costs for sets of horseshoes include at $11,450 initial outlay, and $19,75 per set. They can sell the sets $52.50. If profit is revenue from sales minus manufacturing costs, and the company produces & sales 987 sets of horseshoes, what was their profit?

A. $20,874.25
B. $30,943.25
C. $41,308.50
D. $51,817.50
E. $53,624.25

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

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 production 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