Problema Solution
A florist designs two high-profit arrangements— a funeral wreath and a bridal centerpiece. The company’s employees can complete up to 14 arrangements each day using up to 20 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 $32?
Answer provided by our tutors
let
f =the number of funeral wreaths, f>=0
b =the number of bridal centerpieces, b>=0
The company’s employees can complete up to 14 arrangements:
f + b <= 14
It takes 4 person-hours to complete 1 funeral wreath, and 1 person-hour to complete 1 bridal centerpiece and also using up to 20 total person-hours of labor:
4f + b <= 20
The objective function whose maximum we need to find is:
F(f , b) = 70f + 32b
Since we have the following constrains:
f >=0
b>=0
f + b <= 14
4f + b <= 20
first we need to find the corner points.
Click here to see the graph
the corner points are:
(5, 0), (0, 14) and (2, 12)
For (5,0) we have:
F(5, 0) = 70*5 + 32*0 = $350
For (0,14) we have:
F(0, 5) = 70*0 + 32*14 = $448
For (2,12) we have:
F(2, 12) = 70*2 + 32*12 = 140 + 384 = $524
For maximum profit the florist should produce 2 funeral wreaths and 12 bridal centerpieces.