Luke Corporation produces a variety of products, each within its own division. Last year, the managers at Luke developed and began marketing a new chewing gum, Bubbs, to sell in vending machines. The product, which sells for $$6\mathrm{.}10$ per case, has not had the market success that managers expected, and the company is considering dropping Bubbs.

The product$-$line income statement for the past $12$ months follows:

Revenue $ $14,707,650$

Costs

Manufacturing costs $ $14,448,895$

Allocated corporate costs $($@$5\%)735,38315,184,278$

Product$-$line margin $ $(476,628)$

Allowance for tax $($@$20\%)95,326$

Product$-$line profit $($loss$)$ $ $(381,302)$

All products at Luke receive an allocation of corporate overhead costs, which is computed as $5$ percent of product revenue. The $5$ percent rate is computed based on the most recent year$$s corporate cost as a percentage of revenue. Data on corporate costs and revenues for the past two years follow:

Corporate Revenue Corporate Overhead Costs

Most recent year $ $123,750,000$ $ $6,187,500$

Previous year $77,900,0005,220,065$

Roy O$.$ Andre, the product manager for Bubbs, is concerned about whether the product will be dropped by the company and has employed you as a financial consultant to help with some analysis. In addition to the information given, Mr$.$ Andre provides you with the following data on product costs for Bubbs:

Month Cases Production Costs

$1224,000$ $ $1,167,340$

$2225,7001,188,840$

$3223,4001,197,493$

$4245,0001,213,035$

$5224,5501,215,339$

$6254,0001,236,185$

$7228,7501,211,211$

$8255,7001,254,286$

$9247,3001,252,738$

$10261,1501,264,837$

$11258,7001,269,272$

$12267,7001,299,963$

Required:

a$.$Bunk Stores has requested a quote for a special order of Bubbs. This order would not be subject to any corporate allocation $($and would not affect corporate costs$).$ What is the minimum price Mr$.$ Andre can offer Bunk without reducing profit any further?

b$.$How many cases of Bubbs does Luke have to sell in order to break even on the product?

c$.$Suppose Luke has a requirement that all products have to earn $5$ percent of sales $($after tax and corporate allocations$)$ or they will be dropped. How many cases of Bubbs does Mr$.$ Andre need to sell to avoid seeing Bubbs dropped?

d$.$Assume all costs and prices will be the same in the next year. If Luke drops Bubbs, how much will Luke$$s profits increase or decrease? Assume that fixed production costs can be avoided if Bubbs is dropped.