Question

Carrie runs a restaurant that sells two kinds of cookies. Carrie knows the restaurant must make at least 18 and at most 48 batches of the Fluffy Deliciousness. The restaurant must also make between 2 and 78 batches of the Lemon Puckers. The batches of Fluffy Deliciousness take 13 ounces of sugar, while batches of Lemon Puckers require 8 ounces of sugar. The restaurant only has 1040 ounces of sugar available. If batches of Fluffy Deliciousness generate $2.83 in revenue, and batches of Lemon Puckers generate $2.83, how many batches of the cookies should Carrie have the restaurant make to get the most revenue? Fluffy Deliciousness: Lemon Puckers Best revenue: Get help: Video License Points possible: 3 This is attempt 1 of 10. Submit

Answer 1

Given that both the cookies fetch equal amounts of revenue of
$2.83
each, the best case would arise when the maximum production comes from Lemon Pluckers as they consume less ounces of sugar and contribute to the revenue equally. So, more batches can be produced and more revenue can be generated. But, there is a limit on the maximum number of batched to be produced of Lemon Pluckers i.e. batches.

So, we consider batches as maximum case for the Lemon Pluckers and use this as the first variable to solve the problem.

Let us assume that batches of Lemon Pluckers are made. Each batch requires ounces of sugar.

So, the total amount of sugar used up is ounces.

78 × 8-624

Now, we find that the remaining amount of sugar is ounces.

1040-624 - 416

We have that each batch of Fluffy Deliciousness takes up
13
ounces of sugar so, the number of batches that can be made from the remaining sugar is
32 416 ÷ 13
batches which is within the prescribed limit of Fluffy Deliciousness i.e.
18
to
48
batches.

So, this is the best case and the revenue in this case is

(78 32) × $2.83-$311.3

Fluffy Deliciousness : batches

Lemon Pluckers : batches

Best Revenue :

$311.3