Problem 15-7 Bindley Corporation has a one-year contract to supply motors for al
ID: 422261 • Letter: P
Question
Problem 15-7 Bindley Corporation has a one-year contract to supply motors for all washing machines produced by Rinso Ltd. Rinso manufactures the washers at four locations around the country: New York, Fort Worth, San Diego, and Minneapolis. Plans call for the following numbers of washing machines to be produced at each New York Fort Worth San Diego Minneapolis 75,000 59,000 77,000 60,000 Bindley has three plants that can produce the motors. The plants and production capacities are Boulder Macon Gary 51,000 160,000 70,000 Due to varying production and transportation costs, the profit Bindley earns on each 1,000 units depends on where they were produced and where they were shipped. The following table gives the accounting department estimates of the dollar profit per unit. (Shipment will be made in lots of 1,000.) SHIPPED TO PRODUCED AT NEW YORK FORT WORTH SAN DIEGO MINNEAPOLIS Boulder Macon Gary 20 25 14 13 30 18 28 10 20 Given profit maximization as a criterion, Bindley would like to determine how many motors should be produced at each plant and how many motors should be shipped from each plant to each destinationExplanation / Answer
Let the variables be (in 1,000s) be:
Thus the objective function = (20b1+14b2+18b3+14b4+25m1+28m2+22m3+13m4+8g1+10g2+20g3+30g4)*1000. This is the total profit and has to be maximized.
Constraints are:
Demand side constraints:
1. (b1+m1+g1)*1000=75,000
2. (b2+m2+g2)*1000=59,000
3. (b3+m3+g3)*1000=77,000
4. (b4+m4+g4)*1000=60,000
Supply side constraints:
5. (b1+b2+b3+b4)*1000<=51,000
6. (m1+m2+m3+m4)*1000<=160,000
7. (g1+g2+g3+g4)*1000<=70,000
Lastly all variables >=0 and should be integers
Solving in excel, using the solver function, the following solution is obtained:
(b):
(The above figures are in thousands).
Absolute numbers are:
Profit figures:
Shipped to Produced at New York Fort Worth San Diego Minneapolis Boulder b1 b2 b3 b4 Macon m1 m2 m3 m4 Gary g1 g2 g3 g4