Question

Help please! 10 points!

Answer 1

Let's assume

number of chairs =x

number of tables =y

we are given

Gavin builds furniture for a living. he Sells chairs for $45 and tables for $70 each

So, we can find objective function as

$Z=45x+70y$

now, we can find inequalities

A table requires 10 hours and $15 worth of supplies to make

so, total hours to make table =10y

amount spent on table =15y

It takes Gavin 4 hours and $10 worth of supplies to build each chair

so, total hours to make chair =4x

amount spent on chair =10x

total number of hours to make chair and table =4x+10y

Gavin wants to work for no more than 40 hours per week

so, we get

$4x+10y\leq 40$

spend no more than $80 on materials

so, we get

$10x+15y\leq 80$

so,

objective function:

$Z=45x+70y$

Constraints:

$4x+10y\leq 40$

$10x+15y\leq 80$