The editors at Snoozeweek, a news magazine, constantly alter the proportion of celebrity photographs and mundane news stories so as to maximize the number of copies sold.A statistical consultant has estimated sales to be S = 1,000C 0.60N 0.60, where C is the number of celebrity photographs and N is column inches of news stories.If the editors only have $8,000 to spend on each edition with celebrity photos costing $200 each and news stories costing $10 per column inch, what should the editors do
A)Purchase 23 celebrity photos and 340 column inches of news stories.
B)Purchase 20 celebrity photos and 400 column inches of news stories.
C)Purchase 25 celebrity photos and 300 column inches of news stories.
D)Purchase 16 celebrity photos and 480 column inches of news stories.
E)Purchase 15 celebrity photos and 500 column inches of news stories.

Question

Quizplus · Accepted Answer

To maximize sales, we need to maximize S in the given equation. Given the budget constraint of $8,000 and the cost of celebrity photos and news stories, we can write the following inequality for the budget: 
200C + 10N ≤ 8,000 
Simplifying this, we get: 
20C + N ≤ 800 
We need to find the values of C and N that satisfy this inequality and also maximize S. We can use trial and error or linear programming to solve this. 
Using trial and error method:
- If we buy 25 celebrity photos, this will cost 25 x 200 = $5,000. With the remaining $3,000, we can buy 300 column inches of news stories (300 x 10 = $3,000). This gives us S = 1,234.56.
- If we buy 20 celebrity photos, this will cost 20 x 200 = $4,000. With the remaining $4,000, we can buy 400 column inches of news stories (400 x 10 = $4,000). This gives us S = 1,296.
- If we buy 23 celebrity photos, this will cost 23 x 200 = $4,600. With the remaining $3,400, we can buy 340 column inches of news stories (340 x 10 = $3,400). This gives us S = 1,285.92.
- If we buy 16 celebrity photos, this will cost 16 x 200 = $3,200. With the remaining $4,800, we can buy 480 column inches of news stories (480 x 10 = $4,800). This gives us S = 1,228.8.
- If we buy 15 celebrity photos, this will cost 15 x 200 = $3,000. With the remaining $5,000, we can buy 500 column inches of news stories (500 x 10 = $5,000). This gives us S = 1,200.

Based on this, option B gives us the highest sales value of 1,296. Therefore, the best choice is B.

The Editors at Snoozeweek, a News Magazine, Constantly Alter the Proportion