Question

Please help! Thanks :)

Answer 1

a.
Revenue must be greater than cost.
54x>40x+868

Subtract 40x from both sides
14x>868

Divide both sides by 14
x>62 <===========

b.
63 units must be sold. Remember that units are sold in whole numbers (you can't really buy half a unit). Also, it cannot be 62 units, because that is the point where the company breaks even. 63 is the point where profit is being made.

Answer 2

To start off, let's define a few variables.
r=revenue
c=cost
x=number of units

We know from the problem that r=54x and c=40x+868. The problem also states that the revenue (r) needs to be greater than the cost (c). Using this information we can come up with the inequality.
We know that r>c must be true. Therefore, we can substitute the equation equal to r in for r in the inequality and the equation we have for c in for c in the inequality.
54x>40x+868
Now our inequality has only 1 variable (x).
Now, we must simplify the inequality.
54x>40x+868
Subtract 40x from both sides
54x-40x>40x-40x+868
Combine like terms
14x>868
Divide each side by 14
14x/14>868/14
Simplify
x>62
The answer to part a is x>62.

Now, the answer to part b is not 62 because x must be greater than 62. We also cannot have any partial products. The next whole number is 63. Therefore, 63 products must be sold for the company to make a profit.

The answer to part b is 63 products.