Consider three parts ordered from a single supplier. The data for the items are given in the following table. Assume that there are $52$ weeks in one year and $$10$ is the basic cost of placing an order with one item involved. The inclusion of each additional item costs $$2.$ The holding cost is $$0\mathrm{.}2$ for one dollar of the them tied up in inventory tor one year What is the approximate time interval $($in weeks$)$ between replenishments so that total cost is minimized?

$\backslash$table$[[$Item $i,D_i($units$/$year$),v_i($$$/$unit$)],[1,500,1\mathrm{.}4],[2,4,000,2\mathrm{.}6],[3,2,000,2\mathrm{.}4]]$

a$.0\mathrm{.}0951$

b$.4\mathrm{.}9431$

c$.3\mathrm{.}8791$

d$.0\mathrm{.}0776$

e$.4\mathrm{.}0360$