Assignment

1. The Miller's Tale

Dominic operates the grist mill in Millersville. He will grind grain into flour and keep 25 percent of the flour, which he sells at retail in payment for the milling services. Farms spread in all directions, four farms per square mile.

A farmer can produce eight pounds of wheat with each hour of effort in a given year. Each farmer has ten hours per year to devote to growing, transporting, and milling wheat. The wheat is only useful once milled.

In millng grain on the farm, the farmer can mill three pounds of grain in an hour. Each farmer can transport grain and flour at five miles per hour (one-way-2.5 MPH round trip) up to 200 pounds per load.

What is the radius of the market area of the mill?

What will be the market area in square miles?

Rounding the number of farms to the nearest whole number, how many farms will use Dominic's mill?

2. Betsy McGee launched the Thai Ice Cream (TIC) shop in an area where with 35 potential customers per square mile. Demand for cones is given by cones per year = 3.25 - 0.05 (Price + 7.25 Miles)

(1) If Betzy sets the price at $12.00 for a cone, what will be the market area for TIC?

(2) How many cones will TICsell per year?

(3) If TIC has fixed costs of $90,000 per year and a constant average variable cost of $3.50 per cone, what price (to the nearest cent) will maximize profit? What will be the market area? What will be the maximum profit?