The Bright N Early Coffee Shop sells Regular, Mocha, and Irish blends of coffee. The shop$$s current daily labor cost is $$400,$ the daily equipment cost is $$145,$ and the daily overhead cost is $$175.$ The table below shows the daily demand, along with selling prices and material costs per beverage.

Coffee Product$$Regular$$Mocha$$Irish$$# drinks sold

Price per beverage Materials $($$ per beverage$)$

$375150$ $$2\mathrm{.}25$ $$3\mathrm{.}75$ $$0\mathrm{.}40$ $$0\mathrm{.}90$

$130$ $$4\mathrm{.}00$ $$1\mathrm{.}25$Kayla Jacobson, the manager at Bright N Early Coffee Shop, would like to understand how adding Affogato $($an Italian coffee$-$based dessert that usually takes the form of a scoop of plain milk$-$flavored or vanilla gelato or ice cream topped with a shot of hot espresso$)$ to the menu will alter the shop$$s produc$$vity$.$ Based on her market research, Affogato should atract new customers without nega$$vely impac$$ng the current demand for the exis$$ng products. Assuming that the new equipment is purchased before Affogato is added to the menu, Jacobson has developed new average daily demand and cost projec$$ons$.$ Adding the new product is expected to result in the equipment cost increasing to $$180$ and the overhead cost increasing to $$250.$ The labor cost is not expected to change. The projected daily demands for the new product, as well as selling price and material costs per beverage for the new product line, are shown below.

Coffee Product$$Affogato$$# drinks sold

Price per beverage Materials $($$ per beverage$)$

$50$ $$5\mathrm{.}50$ $$1\mathrm{.}00$a$.$ Calculate and comment on the change in labor and mul$$factor produc$$vity if Affogato is added to the menu. Show your calcula$$ons$.$

b$.$ If everything else remains unchanged, what is the minimum number of units of Affogato that would have to be sold per day to ensure that the mul$$factor produc$$vity increases from its current level. Show your calcula$$ons illustra$$ng this increase.

c$.$ Comment on the feasibility of the number determined in part $($b$).$

d$.$ Describe at least two other ways that Bright N Early Coffee Shop can increase its produc$$vity$.$

Provide a numeric example of each showing the effect on produc$$vity$.$

e$.$ Based upon the data provided, would you recommend adding the new product line? Why or why

not?