A batch of widgets costs p + 15 dollars for a company to pro

Question

A batch of widgets costs p + 15 dollars for a company to produce and each batch sells for p(9 – p) dollars. For which of the following values of p does the company make a profit?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Bunuel · Accepted Answer

Profit = Revenue - Cost = p(9 - p) - (p + 15) = -p^2 + 8p - 15 = -(p-3)(p-5) . At this point we can substitute the options to see for which value is -(p-3)(p-5)>0 OR solve -(p-3)(p-5)>0 . Answer: B. If interested in solving -(p-3)(p-5)>0 : -(p-3)(p-5)>0 --> (p-3)(p-5)<0 --> the "roots" are 3 and 5. "<" sign indicates that the solution lies between the roots: 3if-x-is-an-integer-what-is-the-value-of-x-1-x-2-4x-94661.html#p731476 Hope this helps.

bharatdivvela · Answer

to make profit, selling price should be greater than cost price p(9-p) - p-15 >0 => p^2-8*p+15<0 (p-3)*(p-5)<0 hence p=4

Temurkhon · Answer

Just to be clear after (p-3)*(p-5)<0 we have two options: p<3 and p>5, no solution because no interceptions of intervals p>3 and p<5, so 3

Joc456 · Answer

I have a few questions about this...

When it was time to factor the quadratic I got -p²+8p-15>0. I then divided by -1 so I got p²-8p+15 then got (p-3) and (p-5) so 3 and 5 cannot be the answers. Then you get p²-8p+15<0 so don't we get p<3, p<5

If we try to solve it isn't it p(p-9)-(p+15)? When I plug in 4 the answer is 0.

@temurkohn

(p-3)*(p-5)<0

we have two options:
p<3 and p>5, no solution because no interceptions of intervals
p>3 and p<5, so 3<p<5

How did you get to p>3?

You have p-3<0, wouldn't it be p<3?
Help?

abhimahna · Answer

There are few things that you need to know. (x-a)(x-b) < 0 means a 0 means xb (provided a

anairamitch1804 · Answer

Profit equals revenue minus cost. The company's profit is:
p(9 – p) – (p + 15) = 9p – p2 – p – 15
= – p^2 + 8p – 15
= –(p^2 – 8p + 15)
= –(p – 5)(p – 3)
Profit will be zero if p = 5 or p = 3, which eliminates answers (A) and (C). For p > 5, both (p – 5)
and (p – 3) are positive. In that case, the profit is negative, i.e. the company loses money. The profit
is only positive if (p – 5) and (p – 3) have opposite signs, which occurs when 3 < p < 5.
The correct answer is B.

KarishmaB · Answer

The options give the values of p. Just plug them in to find the value for which p(9 - p) (= revenue) is more than p + 15 (= cost).
When you put p = 3, 3*(9 - 3) = 18 and 3 + 15 = 18. So revenue is not higher. 
When you put p = 4, 4*(9 - 4) = 20 and 4 + 15 = 19. Revenue is higher.

Answer (B)

ScottTargetTestPrep · Answer

Since profit = revenue - cost, or P = R - C, we need to determine a value of p such that revenue > cost. We have that p + 15 = cost and p(9 - p) = revenue. Therefore, the profit is P = p(9 - p) - (p + 15) = 9p - p^2 - p - 15 = -p^2 + 8p - 15.

Notice that the graph of P = -p^2 + 8p - 15 is a parabola that opens downward, so the maximum value is at its vertex. Recall that we can use the formula -b/2a to find the x-value (in this case, the p-value) of the vertex:

p = -b/2a = -8/(2(-1)) = -8/-2 = 4

Answer: B

Abhishek009 · Answer

For Profit CP < SP

So,  p + 15 < p(9 – p)

Or,  p + 15 < 9p – p^2

Now , plug in the values -

(A) 18 < 27 - 9 => 18 < 18 (Not Possible)
(B) 19 < 36 - 16 (Possible)
(C) 20 < 45 - 25 (Not Possible)
(D) 21 < 54 - 36 (Not Possible)
(E) 22 < 63 - 49 (Not Possible)

Hence Answer must be (B)

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A batch of widgets costs p + 15 dollars for a company to pro

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A batch of widgets costs p + 15 dollars for a company to pro

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards