Question

Statement is lengthy, so I have attached the picture of it?

Answer 1

Assuming `Q` is cost of producing, storing `n` items per day.

Cost of manufacturing `C_m` is proportional to quantity produced gives

`C_m = kn`
where `k` is the constant of proportionality for production of `n` items

From the given information

`20000 = kxx200`
`=>k = 20000/200`
`=>k = 100`

`:.C_m = 100n`
As cost of manufacturing is `$100` per item

Storage cost `C_S` is given as proportional to `n^2`

`C_S = k_sn^2`
where `k_s` is the constant of proportionality for storing `n` items

From the given information

`360 = k_sxx(200)^2`
`=>k_s = 360/(200)^2`
`=>k_s = 0.009`
`:.C_S = 0.009n^2`

Overall daily cost `C= "Production" + "Storage" + "Fixed Cost"`

`:.` Overall cost for `n` items

`Q = 100n + 0.009n^2 + 9000`

Rearranging in order of descending value of exponent

`Q = 0.009n^2 + 100n + 9000`
For values of `n" between "0 and 200`