Question

Every year, Danielle Santos sells 93,996 cases of her Delicious Cookie Mix. It costs her $1 per year in electricity to store a case, plus she must pay annual warehouse fees of $3 per case for the maximum number of cases she will store. If it costs her $746 to set up a production run, plus $6 per case to manufacture a single case, how many production runs should she have each year to minimize her total costs?

Answer 1

Solution:-

Given,

M= 93,996

f= $746

K1= $1 per Year

K2= $3 Per Case

Then,

g = √2fM / (K1+2K2)

    =√2*746*93,996/1+(2*3)

    =√140,242,032/1+6

    =√140,242,032/7

=√20,034,576

   = 4476

Hence, g= 4,476 cases per batch

Therefore the number of production is M/g = 93,996/4,476 = 21

So, she must have 21 production run each year to minimize her total​ costs