<p>A few remarks and hints:
We have to assume that each ad in each magazine is viewed by totally different people (totally unreasonable). Given this, then </p>

<p>From your budget constraint, you obtain $c =12-2b$, so you can work with a single decision variable. </p>

<p>Since you are asked about the feasible combinations of $(M,L)$ represented by a straight line, this happens in a diagram with $(M,L)$ measured in the axes. So you have to arrive at an expression of say $M$ as a function of $L$. How do you do this?</p>

<p>Write $L$ (and then also $M$) as a function of $c$ and $b$ (from the information in the question). Use the relation obtained from the budget constraint to eliminate $c$ from both relations. Then solve for $L$ (and for $M$) each as a function of $b$. Equate the two to obtain the function expressing $M$ as a function of $L$.  </p>

<p>Then you can check which of the choices given conforms with this function.</p>

CC BY-SA 3.0
2016-01-17T15:32:06.663Z
Are those two functions of L and M written as a functions of c and b are: $300b+250c=L$ and $1000b+300c=M$?
mkropkowski
CC BY-SA 3.0
2016-01-18T02:10:20.970Z
@mkropkowski I believe those are the correct equations.
majmun
CC BY-SA 3.0
2016-01-17T14:38:44.853Z
2016-01-17T14:48:26.883Z
2016-01-17T14:48:26.883Z
Alecos Papadopoulos
<p>Here is my method, which is less rigorous but perhaps quicker, and I believe allows you to see the answer more easily, at least in this case. It may not be true in every case.</p>

<p>Since the line segment will represent <strong>all</strong> combination of lawyers and M.B.A's that we can reach, it must include the extremes. That is, it must include the cases where we maximize the number of lawyers that we reach, and when we maximize the number of M.B.A's that we reach. In fact, these will be the endpoints (since if we are not maximizing one of these we have to be somewhere in-between). Because of this we can do the following:</p>

<p>1) Figure out how many lawyers we can reach, if we focus on only reaching lawyers. Well, the business magazine lets me reach $300$ lawyers for every $\$700$ I spend. The consumer magazine lets me reach $250$ lawyers for every $\$350$ I spend <strong>or equivalently</strong> $500$ lawyers for every $\$700$ I spend. <strong>This is important</strong> because we are comparing $\$700$ worth of one magazine to $\$700$ worth of another: we are making a $1:1$ comparison, which is necessary.</p>

<p>What the above paragraph tells us is that, if I want to reach as many lawyers as possible, I should spend all my money on the consumer magazine ($500&gt;300$). With a budget of $\$4200$ I can buy $4200/350 = 12$ ads. $12$ ads lets me reach $12*250 = 3000$ layers. So the most lawyers I can reach is $3000$. Additionally, $12$ consumer ads lets me reach $12*300=3600$ M.B.A's, hence one point (one extreme) is 
$$
(3000,3600)
$$</p>

<p>To get the other point, find out how you can reach the most M.B.A's.</p>

<p>One thing to note: The fact that things like $(0,3,600)$ are options should perhaps prompt you to consider maximizing the lawyers reached and maximizing the number of M.B.A's reached (since a $0$ indicates reaching none of one group). Not that doing so will be correct, but if you are stuck such a hint might lead you to the correct answer.</p>

<p>Cheers.</p>

CC BY-SA 3.0
2016-01-18T02:20:32.113Z
2016-01-18T02:20:32.113Z
majmun
<p><strong>Question still unanswered</strong></p>

<p>Ads in the boring business magazine are read by 300 lawyers and 1,000 M.B.A.s. Ads in the consumer publication are read by 250 lawyers and 300 M.B.A.s. If Harry had \$4,200 to spend on advertising, if the price of ads in the boring business magazine were \$700, and if the price of ads in the consumer magazine were \$350, then the combinations of recent M.B.A.s and lawyers with hot tubs whom he could reach with his advertising budget would be represented by the integer values along a line segment that runs between the two points</p>

<p>a.
(3, 600, 0) and (0, 7, 200).</p>

<p>b.
(3, 000, 3, 600) and (1, 800, 6, 000).</p>

<p>c.
(0, 3, 600) and (1, 800, 0).</p>

<p>d.
(3, 600, 4, 200) and (1, 800, 7, 200).</p>

<p>e.
(2, 400, 0) and (0, 6, 000).</p>

<p>My attempt was to find a budget line which is $700b+350c=4200$, where b stand for business magazines and c for consumer ones. But i do not know how this would translate into the answers that are given.</p>

CC BY-SA 3.0
2016-01-16T22:37:43.923Z
This is your budget constraint. You have also a "production function", i.e. contacts generated by the ads. But, it is not clear why in the end the question talks about "recent" MBA's and "lawyers with hot tubs". Do these imply some other restrictions? Moreover, in a dynamic set up, ads will be placed in more than one issue. Will its issue be read by totally different readers? And if we are talking about a single issue per venue, placing two ads in the same issue means that double people will read our message in total? In other words, the problem is not very well posed.
Alecos Papadopoulos
CC BY-SA 3.0
2016-01-17T12:45:47.543Z
No i would not consider recent MBA's and lawyers with hot tubs as additional restrictions, i think that is just a style of the author. I know the problem is not perfectly stated thus i do not know how to answer the rest of your question but i know that the proper answer is B (that is stated in a questionbank it was taken from). On a basis of that what could we say about this question?
mkropkowski
<microeconomics><consumer-theory>
Mix of two ads types
mkropkowski
# Mix of two ads types

(Asked by: username_0 on 2016-01-16)

**Question still unanswered**

Ads in the boring business magazine are read by 300 lawyers and 1,000 M.B.A.s. Ads in the consumer publication are read by 250 lawyers and 300 M.B.A.s. If Harry had \$4,200 to spend on advertising, if the price of ads in the boring business magazine were \$700, and if the price of ads in the consumer magazine were \$350, then the combinations of recent M.B.A.s and lawyers with hot tubs whom he could reach with his advertising budget would be represented by the integer values along a line segment that runs between the two points

a.
(3, 600, 0) and (0, 7, 200).

b.
(3, 000, 3, 600) and (1, 800, 6, 000).

c.
(0, 3, 600) and (1, 800, 0).

d.
(3, 600, 4, 200) and (1, 800, 7, 200).

e.
(2, 400, 0) and (0, 6, 000).

My attempt was to find a budget line which is $700b+350c=4200$, where b stand for business magazines and c for consumer ones. But i do not know how this would translate into the answers that are given.

**Tags:** microeconomics, consumer-theory
> **Comments:**
> **username_1**: This is your budget constraint. You have also a "production function", i.e. contacts generated by the ads. But, it is not clear why in the end the question talks about "recent" MBA's and "lawyers with hot tubs". Do these imply some other restrictions? Moreover, in a dynamic set up, ads will be placed in more than one issue. Will its issue be read by totally different readers? And if we are talking about a single issue per venue, placing two ads in the same issue means that double people will read our message in total? In other words, the problem is not very well posed.  
> **username_0**: No i would not consider recent MBA's and lawyers with hot tubs as additional restrictions, i think that is just a style of the author. I know the problem is not perfectly stated thus i do not know how to answer the rest of your question but i know that the proper answer is B (that is stated in a questionbank it was taken from). On a basis of that what could we say about this question?  

---

## 2 answers

### Answer by username_2 on 2016-01-18. Score: 2 | Accepted answer

Here is my method, which is less rigorous but perhaps quicker, and I believe allows you to see the answer more easily, at least in this case. It may not be true in every case.

Since the line segment will represent **all** combination of lawyers and M.B.A's that we can reach, it must include the extremes. That is, it must include the cases where we maximize the number of lawyers that we reach, and when we maximize the number of M.B.A's that we reach. In fact, these will be the endpoints (since if we are not maximizing one of these we have to be somewhere in-between). Because of this we can do the following:

1) Figure out how many lawyers we can reach, if we focus on only reaching lawyers. Well, the business magazine lets me reach $300$ lawyers for every $\$700$ I spend. The consumer magazine lets me reach $250$ lawyers for every $\$350$ I spend **or equivalently** $500$ lawyers for every $\$700$ I spend. **This is important** because we are comparing $\$700$ worth of one magazine to $\$700$ worth of another: we are making a $1:1$ comparison, which is necessary.

What the above paragraph tells us is that, if I want to reach as many lawyers as possible, I should spend all my money on the consumer magazine ($500>300$). With a budget of $\$4200$ I can buy $4200/350 = 12$ ads. $12$ ads lets me reach $12\*250 = 3000$ layers. So the most lawyers I can reach is $3000$. Additionally, $12$ consumer ads lets me reach $12\*300=3600$ M.B.A's, hence one point (one extreme) is
$$
(3000,3600)
$$

To get the other point, find out how you can reach the most M.B.A's.

One thing to note: The fact that things like $(0,3,600)$ are options should perhaps prompt you to consider maximizing the lawyers reached and maximizing the number of M.B.A's reached (since a $0$ indicates reaching none of one group). Not that doing so will be correct, but if you are stuck such a hint might lead you to the correct answer.

Cheers.


---

### Answer by username_1 on 2016-01-17. Score: 1

A few remarks and hints:
We have to assume that each ad in each magazine is viewed by totally different people (totally unreasonable). Given this, then

From your budget constraint, you obtain $c =12-2b$, so you can work with a single decision variable.

Since you are asked about the feasible combinations of $(M,L)$ represented by a straight line, this happens in a diagram with $(M,L)$ measured in the axes. So you have to arrive at an expression of say $M$ as a function of $L$. How do you do this?

Write $L$ (and then also $M$) as a function of $c$ and $b$ (from the information in the question). Use the relation obtained from the budget constraint to eliminate $c$ from both relations. Then solve for $L$ (and for $M$) each as a function of $b$. Equate the two to obtain the function expressing $M$ as a function of $L$.

Then you can check which of the choices given conforms with this function.

> **Comments:**
> **username_0**: Are those two functions of L and M written as a functions of c and b are: $300b+250c=L$ and $1000b+300c=M$?  
> **username_2**: @mkropkowski I believe those are the correct equations.  

---

