How many possible........

Question

You are assembling cars, and your job is to put the wheels on the vehicles. You have 3520 wheels, 14040 nuts ( 4 nuts needed per wheel) and 1000 car bodies at the start of the day.
How many possible cars can you roll off the assembly line?
What is the limiting reagent in this case?
If you only get to put the wheels on 850 cars that day, what is your productivity?

Answer 1

This is probably a limiting reagent problem from a chemistry class. A more simplified answer is to divide each quantity (wheels, nuts and bodies) by the number needed to make a car. Compare the resulting values. The SMALLEST is the number of cars you can make.

3520÷4 = 880

14,040÷16=877

1000÷1=1000

You can make 877 cars

Answer 2

Let us assume that each car needs 4 wheels.

Since we have 3520 wheels, we can assemble at the most (3520/4) i.e. 880 cars in a day.

Now 3520 wheels will need (3520 X 4) nuts (as each wheel needs 4 nuts).

Thus, total nuts required for 880 cars will be 14080 nuts.

However, we have only 14040 nuts available.

Therefore, we would need (14080 - 14040) = 40 additional nuts in order to build a max total of 880 cars in a day.

Since each wheel needs 4 nuts and we are short of 40 nuts, we will not be able to assemble (40/4) i.e. 10 wheels.

And since each car needs 4 wheels therefore we won't be able to assemble (10/4) = 2.5 cars.

We need to round off 2.5 to the next highest integer in this case, since the number of cars cannot be a decimal value.

Thus, we won't be able to assemble 3 cars in total. 

Thus, in a day we can at max assemble (880 - 3) =  877 cars.

Based on the above explanation we can see that the nuts are the limiting factors in this case.

 

If you get to put only 850 cars in the day, then your productivity percentage is 

(850/877) * 100 = 96.92 %