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 1. From To Evansville Indianapolis South Bend Customer 1 Customer 2 16¢ 40¢ 45¢ 34¢ 30¢ 45¢ Customer 3 26¢ 35¢ 23¢ Table 1: Production & shipping costs Assume that future shipping and production costs are discounted at a rate of 11%per year. Assume that once built, a bakery lasts forever. 1. Formulate an integer optimization model 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).)

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 1. From To Evansville Indianapolis South Bend Customer 1 Customer 2 16¢ 40¢ 45¢ 34¢ 30¢ 45¢ Customer 3 26¢ 35¢ 23¢ Table 1: Production & shipping costs Assume that future shipping and production costs are discounted at a rate of 11%per year. Assume that once built, a bakery lasts forever. 1. Formulate an integer optimization model 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).)

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter7: Systems Of Equations And Inequalities

Section7.2: Systems Of Linear Equations: Three Variables

Problem 61SE: Last year, at Haven's Pond Car Dealership, for a particular model of BMW, Jeep, and Toyota, one...

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