# Thread: Linear equations - HELP

1. ## Linear equations - HELP

OK..so....a plant makes 2 boats, a big one and a small one, and has at most has 1200 labour hrs per week in orders, 1000 hrs working in paint, 500 for motors and 250on seats.

the boats need the following amount of hrs worked on them in each department.

small boats need 0.2 hrs in orders, 0.2 hrs in paint, 0.3 hrs in motors, 0.1 hrs in seats

big boats need 0.4 in orders, 0.5 in pint, 0.1 in motors and 0.1 in seats

assume all produce is sold

.....OK, now to start it i need to form an expression, if small boats(x) go for £80 and big ones(y) for £100, for the sales revenue. Surely this would be revenue = x80 + y80 ? am i wrong?

then it wants the constraints of this problem, and how they're derived??

Please could someone help me out on this!!! thank you.

2. Hello, bobchiba!

A plant makes 2 boats, a big one and a small one.
It has at most has 1200 hrs per week for orders, 1000 hrs working in paint,
500 for motors, and 250 on seats.

The boats need the following amount of hrs worked on them in each department.

Small boats need 0.2 hrs in Orders, 0.2 hrs in Paint, 0.3 hrs in Motors, 0.1 hrs in Seats.

Big boats need 0.4 in Orders, 0.5 in Paint, 0.1 in Motors, 0.1 in Seats.

Assume all boats produced are sold.

Small boats (x) go for $80 and big ones (y) for$100

For revenue, I assume you meant: .$\displaystyle R \;=\;80x + 100y$

Organize the data in a chart . . .

$\displaystyle \begin{array}{c|c|c|c|c|} & \text{Orders} & \text{Paint} & \text{Motor} & \text{Seats} \\ \hline \text{Small }(x) & 0.2 & 0.2 & 0.3 & 0.1 \\ \text{Large }(y) & 0.4 & 0.5 & 0.1 & 0.1 \\ \hline \text{Total} & 1200 & 1000 & 500 & 250 \end{array}$

Now read down the columns and construct the inequalities.

. . $\displaystyle \begin{array}{ccc}0.2x + 0.4y & \leq & 1200 \\ 0.2x + 0.5y & \leq & 1000 \\ 0.3x + 0.1y & \leq & 500 \\ 0.1x + 0.1y & \leq & 250 \end{array}$

and, of course: .$\displaystyle x \geq 0,\;y \geq 0$