Question $28$

$8$ pts

Dawn's Video Diversions wants to expand their DVD rental business. They are considering two options: $(1)$ building another physical store or $(2)$ setting up an on$-$line rental service. For the store option, they will need to purchase $10,000$ DVDs at a total wholesale dealer price of $$15,000.$ In addition to the initial inventory investment, the cost of building a new store is $$60,000.$ For the on$-$line service option, they will need to purchase $15,000$ DVDs at a total wholesale dealer price of $$20,000$ because of the extra rental time to cover mailing. In this $($online service$)$ case, besides the initial inventory investment, additionally, the cost of setting up the on$-$line service platform is $$10,000.$ The $($variable$)$ cost of renting out each DVD from the physical store is estimated to be $65$ cents, while the cost of renting out each DVD from the on$-$line site, including postage, is estimated to be $$1\mathrm{.}60.$ The rental charge for customers $($i$.$e$.,$ revenue$/$sales$)$ per DVD is expected to be $$3\mathrm{.}50$ in both $($physical store and on$-$line service$)$ cases. Show your work$--$using a blank sheet and uploading the worked sheet back onto Canvas$--$for full credit.

a$.$ What is the point of indifference $($in terms of # of rentals$)$ between the store and the on$-$line service options? $(2$ pts$.)$

b$.$ If the rental demand is expected to be $45,000$ DVDs$,$ the better choice $($between the two options$)$ will be $.$

$($For $c$ and $d$ below$)$ You believe that there may be a postage increase that would raise the $\text{'}$on$-$line' rental variable cost to $$1\mathrm{.}70($from $$1\mathrm{.}60).$

c$.$ In this case, what will be the new$/$updated point of indifference $($in terms of # of rentals$)?(2$