A local bagel shop produces bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's baking. Bagel profits are 20 cents each and croissant profits are 30 cents each.
-What is the daily profit when producing the optimal amounts?
A)$580.
B)$340.
C)$220.
D)$380.
E)$420.

Question

Quizplus · Accepted Answer

Let x be the number of bagels produced and y be the number of croissants produced. We want to maximize the daily profit, which is given by the expression: 
P = 0.2x + 0.3y

Subject to the constraints: 
6x + 3y ≤ 6600 (flour constraint) 
1x + 1y ≤ 1400 (yeast constraint) 
2x + 4y ≤ 4800 (sugar constraint)

We can solve this using linear programming methods. However, we can also make some observations to get an idea of what the optimal solution might look like:

- Bagels require more flour and less sugar than croissants, so we might expect the optimal solution to have more bagels than croissants. 
- Both bagels and croissants require the same amount of yeast, so this constraint is less likely to be a limiting factor.

Using these observations, we can try the following combinations: 
- x = 1000 (bagels), y = 800 (croissants), which uses up all the flour and most of the sugar, but still has plenty of yeast left. This yields a profit of P = $340. 
- x = 1200 (bagels), y = 600 (croissants), which uses up all the flour and sugar, but has exactly enough yeast. This yields a profit of P = $360. 
- x = 800 (bagels), y = 1000 (croissants), which uses up all the flour and sugar, but still has plenty of yeast left. This yields a profit of P = $320.

Out of these three options, the first one gives the highest profit of $340. Therefore, the best choice is: 
Answer: B

A Local Bagel Shop Produces Bagels (B) and Croissants (C)