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

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1 Answer
Dec 1, 2017

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#