Q: a factory produces bodies & wheels for standard cars. Each car has to be fitted with one spare wheel. Total number of wheels produced is denoted by W. Number of car bodies is B.
Profit function: $$110B - 3B^2 - 2BW - 2W^2 + 140W$$
Write down the constraint.
Answer: $$lambda(5B - W)$$
Why is this the constraint?
On
One car must fit five wheels: four driving and one spare. Then the constraint is $W=5B$. The Lagrange function is: $$L=profit+\lambda(5B-W).$$
On
It is not an answer !!
You are given the function and a constraint with Lagrange multiplier $\lambda$ and they are linked , so not yet started solving the problem and so nowhere near the answer.
Remove $\lambda $ from last line to get the constraint, viz., $ (5B-W). $ and start solving it.
EDIT1:
Or it may be a typo error for $ \lambda (B-5 W ). $
The text says that each car must be fitted with 1 spare wheel, along with the 4 wheels it would normally have. This means for every 1 body, you must have 5 wheels. So the number of wheels ($W$) is 5 times more than the number of bodies ($B$), i.e. $$W=5B$$ So the constraint is $$\lambda (5B-W)$$