SOLUTION:
We are told that the production cost is directly proportional to quantity.
Thus;
[tex]\begin{gathered} c_1\propto n \\ c_1=kn \end{gathered}[/tex]
We are told that;
It costs $45,000 to produce 900 items, thus;
[tex]\begin{gathered} 45000=900k \\ k=50 \end{gathered}[/tex]
The cost to store n items varies as the square of n, thus;
[tex]\begin{gathered} c_2\propto n^2 \\ c_2=bn^2 \end{gathered}[/tex]
It costs $4050 to store 900 items, thus;
[tex]\begin{gathered} 4050=b(900^2) \\ b=0.005 \end{gathered}[/tex]
There is also a $1000 fixed daily cost; thus the total costs is;
[tex]T=0.005n^2+50n+1000[/tex]
