Problema Solution
A florist designs two high profit arrangements- a funeral wreath and a bridal centerpiece. The company's employees can complete up to 15 arrangements each day using up to 24 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 $75 and the profit on a bridal centerpiece is $44?
Answer provided by our tutors
Let
x = the number of funeral wreaths produced, x>=0
y = the number of bridal centerpiece produced, y>=0
We have the following constrains:
x + y <= 15
4x + y <= 24
The objective function is F(x, y) = 75x + 44y. We need to find the values for x and y for which F(x, y) has maximum.
First we will find the corner points of the system of inequalities:
x + y <= 15
4x + y <= 24
x >= 0
y >=0
The corner points are: (6, 0), (0, 15) and (3, 12).
F(6, 0) = 75*6 + 44*0 = $450
F(0, 15) = 75*0 + 44*15 = $660
F(3, 12) = $885
For maximum daily profit the florist should produce 3 funeral wreaths and 12 bridal centerpieces.