The ACME company manufactured x brooms per month from Januar

Hello ron

We are given that on 1st of each month x brooms are made from Jan to Apr. that gives us \(4x\) brooms in inventory by end of April. On first of each month from May to December \(\frac{x}{2}\) brooms are sold. Therefore we will have

\(4x-\frac{x}{2} = \frac{7x}{2}\) brooms on May 2nd ---> storage cost is $1 per broom per month so in may the company pays \(\frac{7x}{2}\)
Similarly we have \(\frac{7x}{2}-\frac{x}{2} = \frac{6x}{2}\) brooms on June 2 ---> storage cost is \(\frac{6x}{2}\).
July 2nd \(\frac{5x}{2}\)
Continuing this we have \(\frac{x}{2}\) brooms left by Nov 2nd which are sold on Dec 1st, so no more brooms are left on Dec 2nd and no storage costs in december. By adding storage costs as derived above we get

\(\frac{7x}{2}+\frac{6x}{2}+\frac{5x}{2}+\frac{4x}{2}+\frac{3x}{2}+\frac{2x}{2}+\frac{x}{2} = \frac{28x}{2} = 14x\)

Hope this helps!