Question

Peyton runs a restaurant that sells two kinds of pies. Peyton knows the restaurant must make at least 10 and at most 52 batches of the Chocolate Decadence. The restaurant must also make between 2 and 54 batches of the White Chocolate Blizzards. The batches of Chocolate Decadence take 9 ounces of sugar, while batches of White Chocolate Blizzards require 13 ounces of sugar. The restaurant only has 819 ounces of sugar available. If batches of Chocolate Decadence generate $2.86 in revenue, and batches of White Chocolate Blizzards generate $1.23, how many batches of the pies should Peyton have the restaurant make to get the most revenue?

Answer 1

To maximize revenue within the constraints of sugar availability and batch limits, Peyton should make 52 batches of Chocolate Decadence and 27 batches of White Chocolate Blizzards, which will not exceed the limit of 819 ounces of sugar.

Peyton runs a restaurant that must make between 10 and 52 batches of Chocolate Decadence pies and 2 to 54 batches of White Chocolate Blizzards, with a limited sugar supply of 819 ounces. The Chocolate Decadence requires 9 ounces of sugar per batch, while White Chocolate Blizzards need 13 ounces per batch. Moreover, Chocolate Decadence generates $2.86 in revenue per batch while White Chocolate Blizzards generate $1.23. To maximize revenue, Peyton should make as many batches of Chocolate Decadence as the sugar supply allows, since they have a higher revenue per batch. Peyton could use a linear programming method or a solver to find the maximum possible revenue based on these constraints.

First, we need to find the maximum number of Chocolate Decadence pies that can be made with the available sugar. The formula to calculate this is:

Maximum batches of Chocolate Decadence = Total sugar available / Sugar per batch of Chocolate Decadence

Maximum batches of Chocolate Decadence = 819 ounces / 9 ounces per batch

Maximum batches of Chocolate Decadence = 91 batches (rounded down)

However, due to the constraint of making at most 52 batches of Chocolate Decadence, Peyton can only make 52 batches of this type of pie. Next, we calculate how much sugar is left for White Chocolate Blizzards:

Sugar used for Chocolate Decadence = 52 batches * 9 ounces per batch

Sugar used for Chocolate Decadence = 468 ounces

Sugar remaining for White Chocolate Blizzards = Total sugar available - Sugar used for Chocolate Decadence

Sugar remaining for White Chocolate Blizzards = 819 ounces - 468 ounces

Sugar remaining for White Chocolate Blizzards = 351 ounces

Now, to find out how many batches of White Chocolate Blizzards can be made:

Maximum batches of White Chocolate Blizzards = Sugar remaining for White Chocolate Blizzards / Sugar per batch of White Chocolate Blizzards

Maximum batches of White Chocolate Blizzards = 351 ounces / 13 ounces per batch

Maximum batches of White Chocolate Blizzards = 27 batches (rounded down)

Peyton can thus produce 52 batches of Chocolate Decadence and 27 batches of White Chocolate Blizzards without exceeding the sugar limit. To maximize revenue, Peyton should use the sugar to make the highest number of Chocolate Decadence batches allowed (52 batches) since they have a higher revenue per batch compared to White Chocolate Blizzards, and then use the remaining sugar to make 27 batches of White Chocolate Blizzards.