Carlo and Anita make mailboxes and toys in their wood shop. Each mailbox requires 1 hour of work from Carlo and 4 hours from Anita. Each toy requires 1 hour of work from Carlo and 1 hour from Anita. Carlo cannot work more than 12 hours per week and Anita cannot work more than 24 hours per week. If each mailbox sells for $10 and each toy sells for $5, then what is their maximum possible revenue

$80

Step-by-step explanation:

Let the number of hours required to make a mailbox = x

Let the number of hours required to make a toy = y

Each mailbox requires 1 hour of work from Carlo and 4 hours from Anita.

Each toy requires 1 hour of work from Carlo and 1 hour from Anita.

The table below summarizes the information for ease of understanding.

We have the constraints:

Each mailbox sells for $10 and each toy sells for $5.

Therefore, Revenue, R(x,y)=10x+5y

The given problem is to:

Maximize, R(x,y)=10x+5y

Subject to the constraints

The graph is plotted and attached below.

From the graph, the feasible region are:

(0,0), (6,0), (4,8) and (0,12)

At (6,0), 10x+5y=10(6)+5(0)=60

At (4,8), 10(4)+5(8)=80

At (0,12), 10(0)+5(12)=60

The maximum revenue occurs when they use 4 hours on mailboxes and 8 hours on toys.

The maximum possible revenue is $80.

if x = 1, then the answer is 3.5