i)

Question

You are trying to decide if it is worth the investment to make the cakes if it takes 2.5 hours to make each cake and you have 200 hours this summer to devote to creating your product. Write an inequality that represents your time constraint.

*Use x as the variable

Answer 1

The inequality that represents the time constraint is:

2.5x ≤ 200

Where x represents the number of cakes produced.

Answer 2

j)
Solve your inequality from part i

Answer 3

To solve the inequality 2.5x ≤ 200, we need to divide both sides by 2.5:

x ≤ 200/2.5

x ≤ 80

So, the solution to the inequality is:

x ≤ 80

This means that you can make a maximum of 80 cakes within the given time constraint of 200 hours.

Answer 4

k)
Remember it costs $14 to make the cakes and you are selling them for $50 each. If you only spend the 200 hours making the cakes, what was your maximum total profit?

Answer 5

To calculate the maximum total profit, we need to consider both the number of cakes made and the profit per cake.

Since you have a time constraint of 200 hours, we know that the maximum number of cakes you can make is 80, as we determined in part j.

Now, let's calculate the profit per cake. Each cake costs $14 to make, and you sell them for $50 each. So, the profit per cake is:

Profit per cake = Selling price - Cost price = $50 - $14 = $36

To calculate the maximum total profit, we multiply the profit per cake by the maximum number of cakes:

Maximum total profit = Profit per cake x Maximum number of cakes = $36 x 80 = $2880

Therefore, the maximum total profit you can make by spending the 200 hours making the cakes is $2880.