Understanding the argument -
Goal - Maximize profit. Profit = Revenue - Cost. How can we maximize profits? Either we increase revenue or reduce cost? How do we check that we have maximized our profit? If we have to make a revenue of $100 to make $1 as profit vs. another scenario if we can make a profit of $2 per 100 of revenue. The second scenario is preferred to maximize our profit for the given revenue. Profits/revenue may be a good yardstick to check if we have maximized our profits (for the sake of our understanding) other than the absolute numbers.
Plan - Reduce the number of issues by 50%.
So our job is to show that that the profits will decline. P = R-C. So profits can decline if revenues go down or cost increases.
Let's take an example -
Old Situation -
No. of magazines sold earlier - 100
Postage per magazine $6
So total postage cost = $600
Revenue per subscription = $20
Advertisement revenue = $5000
Total revenue = (20*100)+5000 = $7000
Profits = $7000-$600 = $6400
So our profitability is $6400/$7000 = 91.42%
Now, as per the new plan, we reduce the number of units by 50%
Scenario 0 - Advertisement revenue is fixed - Best case scenario.
No. of magazines sold now - 50
Postage per magazine $6 (same)
So total postage cost = $300
Revenue per subscription = $20
Advertisement revenue = $5000
Total revenue = (20*50)+5000 = $6000
Profits = $6000-$300 = $5700
So our profitability is $5700/$6000 = 95%
Scenario 1 - Advertisement revenue is fixed (To evaluate option 1 in the choices)
No. of magazines sold now - 50
Postage per magazine $8 (increase by 1/3)
So total postage cost = $400
Revenue per subscription = $20
Advertisement revenue = $5000
Total revenue = (20*50)+5000 = $6000
Profits = $6000-$400 = $5600
So our profitability is $5600/$6000 = 93.3% (The catch here is that since we reduced the postage cost by 50%, even if the postage cost increases by 33%, we still have a buffer of 17% to play, and while the profitability will be lower than the best case scenario, it'll still be higher than the old situation.
Scenario 2 - Advertisement revenue is per unit ($50 per unit) - To evaluate option D in the choices
No. of magazines sold now - 50
Postage per magazine $6 (stays same)
So total postage cost = $300
Revenue per subscription = $20
Advertisement revenue = $2500
Total revenue = (20*50)+2500 = $3500
Profits = $3500-$300 = $3200
So our profitability is $3200/$3500 = 91.42%
(A) With the new postage rates, a typical issue under the proposed plan would cost about one-third more to mail than a typical current issue would. - If we compare the Old situation (91.42%) and Scenario 1 (93.3%). Scenario 1 is actually better (93.3%) in maximizing profits. We can't do this much in the exam, so another quick way is as we reduced the cost by 50% and now increased it by 33%, we still have a cushion of 17%. This will be a better situation. It's a strengthener and not a weakener that we are looking for.
(B) The majority of the magazine's subscribers are less concerned about a possible reduction in the quantity of the magazine's articles than about a possible loss of the current high quality of its articles. - But the argument says that the quality will remain the same. Distortion.
(C) Many of the magazine's long-time subscribers would continue their subscriptions even if the subscription price were increased. - The argument said that the subscription will remain the same. Distortion.
(D) Most of the advertisers that purchase advertising space in the magazine will continue to spend the same amount on advertising per issue as they have in the past. This is our Scenario 2 (91.42%). The absolute profits have not only reduced w.r.t. new plan (Scenario 0), but the profitability is also lower. As per the new plan, the profits should be $5700, but if advertising is per issue, the profits plummet to $3200. The trap words here in the argument are "Market research shows that no advertisers will be lost if the magazine's plan is instituted." But the deception here is okay; the number of advertisers can remain the same, but will their spending remain the same? That's what this option exposes.
(E) Production costs for the magazine are expected to remain stable - It's good if they remain stable. But if they are unstable, it'll likewise impact the old situation and new plans.
Let's plug the numbers for our understanding
Old Situation (including production cost)
No. of magazines sold earlier - 100
Postage per magazine $6
So total postage cost = $600
The production cost per magazine $5
Production cost for 100 magazines - $500
Revenue per subscription = $20
Advertisement revenue = $5000
Total revenue = (20*100)+5000 = $7000
Profits = $7000-$600-$500 = $5900
So our profitability is $5900/$7000 = 84.2%
Now, as per the new plan, we reduce the number of units by 50%
Scenario 3 - Advertisement revenue is fixed - Best case scenario.
No. of magazines sold now - 50
Postage per magazine $6 (same)
So total postage cost = $300
The production cost per magazine is $5
Production cost for 50 magazines - $250
Revenue per subscription = $20
Advertisement revenue = $5000
Total revenue = (20*50)+5000 = $6000
Profits = $6000-$300 - $250= $5450
So our profitability is $5450/$6000 = 90%
The new plan is still better as this option impacts both scenarios equally. At best, this is a distortion.
Now, is it required to do so many calculations in the exam? No way. But when we are practicing, let's get to the depth of the problem so that, hopefully, we can think in the right direction when we see such complex arguments.