A florist designs two high-profit arrangements

Question

A florist designs two high-profit arrangements— a funeral wreath and a bridal centerpiece. The company’s employees can complete up to 18 arrangements each day using up to 27 total person-hours of labor. It takes 4 person-hours to complete 1 funeral wreath, and 1 person-hour to complete 1 bridal centerpiece. How many of each type of arrangements should the florist produce daily for maximum profit, if the profit on a funeral wreath is $70and the profit on a bridal centerpiece is $34?

 

Number of bridal centerpieces...

Number of funeral wreath..

Answer 1

Since profits on the centerpieces are $34 and it takes 1 person-hour to make it, that's creating $34 profit/person-hour.

Since profits on the wreath are $70 and it takes 4 person-hours to make it, that's creating $17.5 profit/person-hour.

 

It looks like the florist would rather make as many centerpieces as possible, but we can only make 18 arrangements total.

 

Let's see what the math says by building some equations. I'll use w for wreaths and c for centerpieces. Because we want to use every one of the 27 hours, we can keep track of how many of those hours were used for each type of arrangement:

 

c+4w=27

c+w≤18

 

Using our first two equations, we can solve for c and substitute into the second equation

 

c=27-4w

(27-4w)+w≤18

27-3w≤18

 

Remember our rules for inequalities here: multiplying or dividing by a negative reverses the inequality.

 

-3w≤-9

w≥3

 

So the math says we must make at least 3 wreaths. We want as few wreaths as possible, so let's spend 12 hours making those 3, meaning we can spend the other 15 hours making 15 centerpieces.

 

3 wreaths = $210

15 centerpieces = 15*34=$510