Problema Solution
Carlo and Anita make mailboxes and toys in their craft shop near Lincoln. Each mailbox requires 3 hours of work from Carlo and 4 hours from Anita. Each toy requires 3 hours of work from Carla and 1 hour from Anita. Carlo cannot work more that 18 hours per week and Anita cannot work more than 12 hours per week. If each mailbox sells for $9 and each toy sells for $17, then how many of each should they make to maximize their revenue? what is their maximum revenue?
Answer provided by our tutors
Let
m = the number of mailboxes, m>=0
t = the number of toys, t>= 0
We have the following limitations:
3m + 3t <= 18
4m + t <= 12
The objective function (the revenue) is F(m, t) = 9m + 17t
Click here to see the graph of the system of 4 inequalities:
3m + 3t <= 18
4m + t <= 12
t >= 0
m >= 0
We need to find the corner points:
The corner points are: (0, 0), (3, 0), (0, 6), (2, 4)
F(0, 0) = 0
F(3, 0) = 9*3 = $27
F(0 , 6) = 17*6 = $102
F(2 , 4) = 9*2 + 17*4 = $86
To maximize the revenue they should make 6 toys.
The maximum revenue is $102.