Problem Set Break$-$Even

$1.$ The O$$Neill Shoe manufacturing Company will produce a special$-$style shoe if the

order size is large enough to provide a reasonable profit. For each special$-$style

order, the company incurs a fixed cost of $$1,000$ for the production setup. The

variable cost is $$30$ per pair, and each pair sells for $$40.$

a$)$ Develop a mathematical model for the total cost of producing pairs

shoes.

b$)$ Develop a mathematical model for the total profit realized from an order

for pairs shoes.

c$)$ How large must the shoe order be before O$$Neill will break even? Use the

Table Command in Excel to perform sensitivity analysis for a range of

volume from $10-300$ in increments of $10.$

$2.$ Eastman Publishing Company is considering publishing a paperback textbook on

spreadsheet applications for business. The fixed cost of manuscript preparation,

textbook design, and production setup is estimated to be $$80,000.$ Variable

production and material costs are estimated to be $$3$ per book. Demand over the

life of the book is estimated to be $4,000$ copies. The publisher plans to sell the text

to college and university bookstores for $$20$ each.

a$)$ What is the break$-$even point?

b$)$ What profit$/$loss can be anticipated with a demand of $4,000$ copies?

c$)$ With a demand of $4,000$ copies, what is the minimum price per copy that

the publisher must charge to breakeven?

d$)$ If the publisher believes that the price per copy would be increased to

$$25\mathrm{.}95$ and not affect the anticipated demand of $4,000$ copies, what action

would you recommend? What profit or loss can be anticipated?

$3.$ Preliminary plans are underway for the construction of a new stadium for a major

league baseball. City officials have questioned the number and profitability of the

luxury corporate boxes planned for the upper deck of the stadium. Corporations

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