E$8-28$A$.$ Determine product mix for retailer$-$two stocking scenarios $($Learning Objective $5)$

Each morning, Larry Imery stocks the drink case at Larry$$s Beach Hut in Charlotte, North Carolina. Larry$$s Beach Hut has $110$ linear feet of refrigerated display space for cold drinks. Each linear foot can hold either five $12-$ounce cans or three $20-$ounce plastic or glass bottles. The beverage stands sells three types of cold drinks:

$1.$ Cola in $12-$oz$.$ cans for $$1\mathrm{.}40$ per can$2.$ Bottled water in $20-$oz$.$ plastic bottles for $$1\mathrm{.}75$ per bottle$3.$ Orange juice in $20-$oz$.$ glass bottles for $$2\mathrm{.}10$ per bottle

Larry$$s Beach Hut pays its suppliers the following:

$1.$ $$0\mathrm{.}20$ per $12-$oz$.$ can of cola$2.$ $$0\mathrm{.}45$ per $20-$oz$.$ bottle of water$3.$ $$0\mathrm{.}75$ per $20-$oz$.$ bottle of orange juice

Larry$$s Beach Hut$$s monthly fixed expenses include the following:

The data from the table are as follows:

The beverage stand can sell all drinks stocked in the display case each morning.

Requirements

$1.$ What is the constraining factor at Larry$$s Beach Hut? What should Larry stock to maximize profits? What is the maximum contribution margin he could generate from refrigerated drinks each day?$2.$ To provide variety to customers, suppose Larry refuses to devote more than $60$ linear feet and no less than $20$ linear feet to any individual product. Under this condition, how many linear feet of each drink should be sto