24 Breadco Bakeries is a new bakery chain that sells bread to customers throughout the state of Indiana. Breadco is considering building bakeries in three locations:

Evansville, Indianapolis, and South Bend. Each bakery can bake as many as 900,000 loaves of bread each year. The cost of building a bakery at each site is $5 million in Evansville,

$4 million in Indianapolis, and $4.5 million in South Bend.

To simplify the problem, we assume that Breadco has only three customers, whose demands each year are 700,000 loaves (customer 1); 400,000 loaves (customer 2); and 300,000 loaves (customer 3). The total cost of baking and shipping a loaf of bread to a customer is given in Table 21.

Assume that future shipping and production costs are discounted at a rate of 11

1 9

% per year. Assume that once built, a bakery lasts forever. Formulate an IP to minimize Breadco’s total cost of meeting demand (present and future). (Hint: You will need the fact that for x 1, a  ax  ax2  ax3   a/(1  x).) How would you modify the formulation if either Evansville or South Bend must produce at least 800,000 loaves per year?