Sweet Dreams Bakery was started five years ago by Della Fontera who was known for her breads, sweet rolls, and personalized cakes. Della had kept her accounting system simple, believing that she had a good intuitive handle on costs. She had been using the following formula to describe her monthly overhead costs:

Overhead cost $=$ $$7,800+$ $$7\mathrm{.}5($direct labor hours$)$

For breads and sweet rolls that were available in the bakery case each day, she applied a standard pricing system. For special orders, however, Della needed her cost formula to help her come up with an estimated cost for the personalized cake or wedding cake. To that cost, she applied a markup percentage.

Lately, however, the increase in the variety of orders and the elaborateness of the wedding cakes made her wonder if a more sophisticated view of costs would help her in planning, budgeting, and pricing.

After some late$-$night discussions with her workers, Della determined that Sweet Dreams' expansion into wedding cakes and gift baskets had made special orders a more complex operation. The various shapes of the wedding cake tiers had required Della's investing in different$-$sized cake pans, as well as decorating tips for icing. The different icing patterns and elaborate designs took much more time for icing, as well. In addition, while a five$-$year$-$old's birthday cake just requires that the child's name and $($possibly$)$ the superhero's name are spelled correctly, a wedding cake is a once$-$in$-$a$-$lifetime item that must achieve perfection. Gift baskets required Della to stock baskets, cellophane, and bows. Then when an order came in$,$ a worker had to stop baking to arrange the muffins and breads artfully in the basket, wrap it$,$ and tie the bow. While it seemed simple enough, this took time and thought. Thus, the number of direct labor hours was still an important variable, but so were the number of wedding cakes and gift baskets. Della rummaged through her college textbooks and found information on regression. Then, with help from one of her computer savvy workers, she ran multiple regression tables for the past $24$ months of data for Sweet Dreams for three independent variables: number of direct labor hours, the number of wedding cakes, and the number of gift baskets. The following printout was obtained:

Parameter Estimate t for Ho

Parameter $=0$ Pr $>$ t Standard Error

of Parameter

Intercept $$1,98093\mathrm{.}000\mathrm{.}0001264\mathrm{.}00$

Number of direct labor hours $($X$1)$ $$2\mathrm{.}553\mathrm{.}600\mathrm{.}00500\mathrm{.}89$

Number of wedding cakes $($X$2)$ $$67\mathrm{.}305\mathrm{.}580\mathrm{.}00503\mathrm{.}19$

Number of gift baskets $($X$3)$ $$2\mathrm{.}302\mathrm{.}960\mathrm{.}02500\mathrm{.}75$

R$2=0\mathrm{.}92$

Se $=65$

Observations: $24$

Required:

$1.$ Write out the cost equation for Sweet Dreams$$ monthly overhead cost.

Y $=$ $fill in the blank $1$

$+$ $fill in the blank $2$

x$1+$ $fill in the blank $3$

x$2+$ $fill in the blank $4$

x$3$

$2.$ Suppose that next month Sweet Dreams expects to have $500$ direct labor hours, $40$ wedding cakes, and $20$ gift baskets. What is the expected overhead? $($Round your answer to the nearest dollar amount.$)$

$fill in the blank $5$

$3.$ What is your evaluation of the cost equation that was developed for the cost of overhead based on the R$2$ in this equation?

Suppose that Sweet Dreams charges an extra $$2\mathrm{.}60$ to prepare a gift basket. This charge is in addition to the price charged for the items $($e$.$g$.,$ muffins$)$ that the customer chooses to put into the basket.

Can Della compare the additional cost of a gift basket $($$$2\mathrm{.}30)$ to the price charged of $$2\mathrm{.}60.$