Multiple$-$Product Value Streams, Product Costing, Creating Available Capacity

Sixty employees $($all CPAs$)$ of a local public accounting firm eat lunch at least twice weekly at a very popular pizza restaurant. The pizza restaurant recently began offering discounts for groups of $15$ or more. Groups would be seated in a separate room, served individual bowls of salad costing $$2$ each, pitchers of root beer costing $$3$ each $($each pitcher has a five$-$glass capacity$),$ and medium, two$-$topping pizzas for $$10(10$ slices each$).$ The food would have to be ordered in advance.

Thirty of the CPAs commit to eating three slices of pizza, three glasses of root beer, and one bowl of salad $[$a consumption pattern of $(3,3,1)].$ The other $30$ are more hearty eaters and commit to seven slices of pizza, two glasses of root beer, and one bowl of salad $[$a consumption pattern of $(7,2,1)].$ Each member of the group must pay an assessed amount for the lunch.

After some detailed polling among the $60,$ four types of eaters were identified: two types of light eaters and two types of heavy eaters. The consumption patterns for each group are given $($slices of pizza, glasses of root beer, and bowls of salad$)$: Light Eaters $($Group A$)$: A$1=(2,2,1)$ and A$2=(3,3,1)$; Heavy Eaters $($Group B$)$: B$1=(6,3,1)$ and B$2=(7,2,1).$ There are an equal number of CPAs in each of the four groups.

Required:

$1.$ Calculate the average lunch cost for each CPA in each of the two groups, A and B$,$ then compare these averages to the ABC cost assignments. Round your answers to the nearest cent if rounding is required. In your calculations, round the number of pizzas to the nearest whole pizza.

Average cost for group A $($light eaters$)$: $ per person

ABC cost for sub$-$group A$1$: $ per person

ABC cost for sub$-$group A$2$: $ per person

Average cost for group B $($heavy eaters$)$: $ per person

ABC cost for sub$-$group B$1$: $ per person

ABC cost for sub$-$group B$2$: $ per person

$2.$ Suppose that members of the heavy$-$eating group $($Group B$)$ decided that they were eating more than necessary for their health and well$-$being and decided to reduce their total calories. They therefore agreed to reduce consumption of pizza by one slice and consumption of root beer by one glass for each member of the group. Relative to the original order, how much extra capacity exists?

Excess capacity: slices of pizza and glasses of root beer.

If the excess capacity is eliminated by reducing the order, what is the new average cost? Round your answer to the nearest cent if rounding is required.

$ per person.

Suppose that the decision is to use the extra capacity to invite four guests $($two of Type B$1$ and two of Type B$2)$ to lunch $($at the cost of the CPAs$).$ If the original order is used as the benchmark cost, what is the extra cost of the guest program?

$ per guest.