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Single and Dual Charging Rates

Jeff McMillan owns a small neighborhood shopping mall. Of the $10$ store spaces in the building, seven are rented by boutique owners and three are vacant. Jeff has decided that offering more services to stores in the mall would enable him to increase occupancy. He has decided to use one of the vacant spaces to provide, at cost$,$ a gift$-$wrapping service to shops in the mall. The boutiques are enthusiastic about the new service. Most of them are staffed minimally, which means that every time they have to wrap a gift, phones go unanswered and other customers in line grow impatient. Jeff figured that the gift$-$wrapping service would incur the following costs: the store space would normally rent for $$1,700$ per month, part$-$time gift wrappers could be hired for $$1,600$ per month, and wrapping paper and ribbon would average $$1\mathrm{.}40$ per gift. The boutique owners estimated the following number of gifts to be wrapped per month.

Store Number of Gifts

Wrapped per Month

The Stationery Station $175$

Arts & Collectibles $400$

Kid$-$Sports $100$

Java Jim's $75$

Designer Shoes $20$

Cristina's Closet $130$

Alan's Drug and Sundries $100$

After the service had been in effect for six months, Jeff calculated the following actual average monthly number of gifts wrapped for each of the stores.

Store Actual Average Number of

Gifts Wrapped per Month

The Stationery Station $160$

Arts & Collectibles $420$

Kid$-$Sports $240$

Java Jim's $10$

Designer Shoes $50$

Cristina's Closet $200$

Alan's Drug and Sundries $450$

Required:

$1.$ Calculate a single charging rate, on a per$-$gift basis, to be charged to the shops. If required, round your final answer to the nearest cent.

$fill in the blank $1$

$4\mathrm{.}7$

per gift

Based on the shops' actual number of gifts wrapped, how much would be charged to each shop using the single charging rate?

Store Total Charge

The Stationery Station $fill in the blank $2$

$752$

Arts & Collectibles fill in the blank $3$

$1,974$

Kid$-$Sports fill in the blank $4$

$1,128$

Java Jim's fill in the blank $5$

$47$

Designer Shoes fill in the blank $6$

$235$

Cristina's Closet fill in the blank $7$

$940$

Alan's Drug and Sundries fill in the blank $8$

$2,115$

$2.$ Based on the shops' actual number of gifts wrapped, how much would be charged to each shop using the dual charging rate? If required, round the allocation percentages to $4$ decimal places and round your computed allocation amount to the nearest cent.

Store Total Charge

The Stationery Station $fill in the blank $9$

Arts & Collectibles fill in the blank $10$

Kid$-$Sports fill in the blank $11$

Java Jim's fill in the blank $12$

Designer Shoes fill in the blank $13$

Cristina's Closet fill in the blank $14$

Alan's Drug and Sundries fill in the blank $15$

$3.$ Which shops would prefer the single charging rate? Why?

The Stationery Station

Arts & Collectibles

Kid$-$Sports

Java Jim's

Designer Shoes

Cristina's Closet

Alan's Drug and Sundries

a and d

In the single rate method, fixed costs are included in the rate based on

estimated

usage. The single charging rate assigns less of the fixed cost to the shops using

less

of the service.