Question

The Father Domino Company sels copying machines. A major factor in making a sale is Domino's quick service. Domino sells copiers in six cties: 1. Boston, 2. New York, 3. Philadelphia, 4. Washington, 5. Providence, and 6. Atlantic City. The annual sales of copiers (in number of copiers sold) projected depend on whether a service representative is within 150 miles of a city (see table below. within 150 miles? 1. Boston 2. New Vork 3. Philadelphia 4. Washington 5. Providence 6. Allantic City 450 300 1,000 750 400 900 800 700 500 200 No 700 Each copier costs $500 to produce and sells tor $1,000. The annual cost per service represertative is $80,000. Domino must determine in which of its markets to base a service representative. Only Boston, New York, Philadelphia, and Washington are under consideration as bases for service representative. The distance (in miles) between the cibes is shown below 1. Boston 2. New York 3. Philadelphia 4. Washington 441 241 146 1. Boston 2. New York 3. Phladelphia 310 4. Washington 441 5. Providence 6 Allantic City 350123 310 241 186 146 376 178 47 255 Formulate an appropriate mathematical modelくshould not be nonínear) that wil het, Domino maximize annual profits. Remark: Your model should be a strong formulation

Answer 1

Profit per copier = selling price - cost = 1000 - 500 = $ 500

List of markets which can be service by representative based on city is following:

Market	Can be service by representative based in city
1. Boston	Boston
2. New York	New York, Philadelphia
3. Philadelphia	New York, Philadelphia, Washington
4. Washington	Philadelphia, Washington
5. Providence	Boston
6. Atlantic ciy	New York, Philadelphia

Mathematical model is following:

Let Xi = 1, if a service representative is based in city i , otherwise Xi = 0

Yj = 1, if any representative is within 150 miles of market in city j, otherwise Yj = 0

Max 500*(500+750+700+450+200+300+(700-500)Y1+(1000-750)Y2+(900-700)Y3+(800-450)Y4+(400-200)Y5+(450-300)Y6)-80000(X1+X2+X3+X4)

s.t.

X1-Y1>=0

X1+X2-Y2>=0

X2+X3+X4-Y3>=0

X3+X4-Y4>=0

X1-Y5>=0

X2+X3-Y6>=0

Xi, Yj binary