10 points! 10: gavin builds furniture for a living. he sells chairs for $45 and tables for $70 each. it takes gavin 4 hours and $10 worth of supplies to build each chair. a table requires 10 hours and $15 worth of supplies to make. gavin wants to work for no more than 40 hours per week and spend no more than $80 on materials. write a system of inequalities and state 3 possible combos.

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

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

spend no more than $80 on materials

so, we get

so,

objective function:

Constraints:

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus