A local outdoor vegetable stand has exactly $1,000$ square feet of space to display three vegetables: tomatoes, lettuce, and zucchini. The appropriate data for these items are given in the following table.Determine the space requirements of lettuce: $w_2=[,]sqft$ per unit.

Tomatoes Lettuce Zucchini

Annual Demand $($lbs$)8501280630$

Cost per lb $$0\mathrm{.}29$ $$0\mathrm{.}45$ $$0\mathrm{.}25$

The setup cost for replenishment of the vegetables is $$100$ in each case, and the space consumed by each vegetable is proportional to its costs, with tomatoes requiring $0\mathrm{.}5$ square foot per lb$.$ The annual interest rate used for computing holding cost is $25\%.$

What are the optimal quantities that should be purchased of these three vegetables?

$1)$ Determine the space requirements of lettuce: w$2=[]$ sq ft per unit.

$2)$ Determine the space requirements of zucchini: w$3=[]$ sq ft per unit.

$3)$ The $($theoretical$)$ EOQ value for tomatoes : EOQ$1=[]$

$4)$ The $($theoretical$)$ EOQ value for lettuce : EOQ$2=[]$

$5)$ The $($theoretical$)$ EOQ value for lettuce : EOQ$3=[]$

$6)$ Determine the multiplier : m$=[]$

$7)$ The optimal order quantity for tomatoes : Q$1=[]$

$8)$ The optimal order quantity for lettuce : Q$2=[]$

$9)$ The optimal order quantity for zucchini : Q$3=[]$