1. ## Constraint Equation

John can make a profit of $7 per chair and$12 per desk. He has at most 48 hrs working time available. It takes 3 hrs to make a chair and 2 hrs to make a desk. Write the objective function and constraints necessary to determine how many chairs and desks he should make to maximize profit.

X=Chairs
Y=desks

I cant figure out the constraints other than:

3x+2y<48
7x+12y>0
x>0
y>0

2. Hello, JennM!

You need a small adjustment . . .

John can make a profit of $7 per chair and$12 per desk.
He has at most 48 hrs working time available.
It takes 3 hrs to make a chair and 2 hrs to make a desk.
Write the objective function and constraints necessary to determine
how many chairs and desks he should make to maximize profit.

$x$ = chairs . $y$ = desks

I cant figure out the constraints other than:

$3x+2y\:<\:48$
$7x+12y\:>\:0$ . . . . no
$x\:>\:0,\;y\:>\:0$

Objective function: . $P \:=\:7x+12y$ . (profit)

Constraints: . $\begin{Bmatrix}3x + 2y \:\leq \:48 \\
x \:\geq \:0 \\ y \:\geq \:0 \end{Bmatrix}$

3. I was trying to get the Greater n less than or equal to signs... Couldnt find them. So basically I had the answer but was confused thanks for the help