A local outdoor vegetable stand has exactly $1200$ square feet of space to display $3$ vegetables:

tomatoes, lettuce, and zucchini. The appropriate data for these items is given in the following table.

Tomatoes Lettuce Zucchini

Annual Demand $($in lb$)7508001000$

Cost $($per lb$)$ $$0\mathrm{.}40$ $$0\mathrm{.}70$ $$0\mathrm{.}60$

Space requirement $($in ft$2/$lb$)0\mathrm{.}40\mathrm{.}651$

 

The setup cost for replenishment of the vegetables is $$275$ for each type of vegetable. The annual interest 

 

 rate used for computing holding costs is $20$ percent.

 

 

a$)$ Find the individual EOQs for each vegetable without regard to the display space constraint.

b$)$ What is the total display space required by the EOQ amounts in part a$?$

c$)$ Now consider the display space constraint; what are the optimal quantities that should be

purchased of these three vegetables?

d$)$ What is the maximum amount $($in $$/$ft $2)$ this vegetable vendor should be willing to pay for

additional display space?