Text for Questions $1-12$

Horatio Alger has just become product manager for Brand $x.$ Brand $x$ sells a product

to a wholesaler; the wholesaler sells it to a retailer; and ${?}^2$ the retailer sells it to the

consumer. The retail price is $$1\mathrm{.}00.$ Retail margins on the product are $33\%,$ while

wholesalers take a $12\%$ margin.

Brand $x$ and its direct competitors sell a total of $20$ million units annually; Brand $x$

has $24\%$ of this market.

Variable costs: Variable manufacturing costs for Brand $x$ are $$0\mathrm{.}09$ per unit.

Salespeople are paid entirely by a $10\%$ commission $($i$.$e$.,10\%$ of the price at which

Brand $x$ sells the product to the wholesaler$).$ Shipping costs, breakage, insurance,

and so forth are $$0\mathrm{.}02$ per unit.

Fixed manufacturing costs $($per year$)$ are $$900,000.$ The advertising budget $($per year$)$

for Brand $x$ is $$500,000.$ The Brand $x$ product manager's salary and expenses total

$$35,000($per year$).$