Each morning, Mike Rouse stocks the drink case at Mike's Beach Hut in Virginia Beach, Virginia. Mike's Beach Hut has $105$ linear feet of refrigerated display space for cold drinks. Each linear foot can hold either five $12-$ounce cans or four $20-$ounce plastic or glass bottles.

$($Click the icon to view the information on the cold drinks.$)$

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

Requirement $2.$ To provide variety to customers, suppose Mike refuses to devote more than $70$ linear feet and no less than $5$ line linear feet of each drink should be stocked? How many units of each product will be available for sale each day?

Show how Mike should stock his shelves, based on each product's contribution margin $($CM$)$:

$1$st stock maximum contraint of $$ linear ft$.$ with product having the $CM$: $$

Next minimum constraint of $q,$ linear $ft.$ with product having the $CM$:

Stock the remaining $$ linear $ft.$ with product having the $CM$ :

Now calculate the units available for sale based on the product mix determined above.

$\backslash$table$[[,$Units for sale$],[$cola$-$cola in $12$ oz$.$ cans:,cans$],[$energize$-$ade in $20$ oz$.$ bottles:,bottles$],[$best$-$cola in $20$ oz$.$ bottles:,bottles$]]$

Requirement $3.$ Assuming the product mix calculated in Requirement $2,$ what contribution margin will be generated from refriger whole dollar.$)$

Contribution Margin

$\backslash$table$[[$cola$-$cola in $12$ oz$.$ cans:,Contribution Margin$],[$energize$-$ade in $20$ oz$.$ bottles:,$],[$best$-$cola in $20$ oz$.$ bottles:,$],[$Total$,]]$

Data table

The beverage stand sells three types of cold drinks:

Cola $-$ Cola in $12-0z.$ cans for $$1\mathrm{.}45$ per can

Energize $-$ Ade in $20-$oz$.$ plastic bottles for $$1\mathrm{.}70$ per bottle

Best $-$ Cola in $20-$oz$.$ glass bottles for $$2\mathrm{.}30$ per bottle

Mike's Beach Hut pays its suppliers the following:

$$0\mathrm{.}20$ per $12-0z.$ can of cola $-$ cola

$$0\mathrm{.}40$ per $20-$ oz$.$ bottle of energize $-$ ade

$$0\mathrm{.}80$ per $20-0z.$ bottle of best $-$ cola

Mike's Beach Hut's monthly fixed expenses include the following:

$\backslash$table$[[$Hut rental. $............,$$$,370],[$Refrigerator rental,,$75],[$Mike$\text{'}$s sala,,$1,400],[$Total fixed expenses,$$,1,845]]$