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![Q 3. The Avalon Floor Cleaner nteger Programming 120 points) to dectermine is trying to determine the number of salespeople it s he cose nit adei and y has 100 Sonthe East, the Midwest, and the West. The companss olume nts to assign to the three regions. The annual average un in the West. Because travel distances, o annual cost of having a salespers each region is 25,000 in the East, 18,000 in the Midwest and St.o omny as person is $6,000 in the East, $11.000 in the Midwest, and $7.,000 company had es, costs of living, and other factors vary among the three regions, the budgeted must haoch region To ensure nationwide exposure its product, the company wants to kno average units sold. company has decided that each region must have at least 10 salespeopte many salespeople to allocate to each region to maximize tota 15 points] Formulate a complete integer programming model for this problem b. [ points) How many salespeople are assigned to the East?](https://media.cheggcdn.com/media%2Ff88%2Ff888855f-de83-47ab-a340-d65ae2634f78%2Fimage)
The Avalon Floor Cleaner Company is trying to determine the number of salespeople it should allocate to its three regions mdash the East, the Midwest, and the west. The company has 100 salespeople that it wants to assign to the three regions. The annual average unit sales volume achieved by a salesperson in each region is 25,000 in the East, 18,000 in the Midwest and 31,000 in the West. Because travel distances, cost of living, and other factors vary among the three regions, the annual cost of having a salesperson is $6,000 in the East, $11,000 in the Midwest, and $7,000 the West. The company has $700,000 budgeted for expenses. To ensure nationwide exposure its product, the company has decide that each region must have at least 10 salespeople. The company wants to know how many salespeople to allocate to each region to maximize total average units sold. Formulate a complete integer programming model for this problem How many salespeople are assigned to the East?
Expert Answer
Decision Variable:
Let, E = number of salesperson (SP) required in east region
M = number of salesperson (SP) required in Midwest region
W = number of salesperson (SP) required in West region
Objective Function: Objective is to maximize the total units sales of the company for the regions. The total sales function is given as follows:
Max Z = 25,000E + 18,000M + 31,000W
Subject To:
| Constraint | Equation |
| Sales Budget | 6000E + 11000M + 7000W <= 700,000 |
| Min. SP in East | E >= 10 |
| Min. SP in Midwest | M >= 10 |
| Min. SP in West | W >= 10 |
| Non-negative | E, M, W >= 0 |
| Integer DV | E, M, and W all are integers |
Excel Model and Solver Solution:
Copy-Paste following table in Excel:
| Region | East | Midwest | West | |||
| DV | E | M | W | |||
| No. of Salesperson | 0 | 0 | 0 | Total Sales | ||
| Sales volume per salesperson | 25000 | 18000 | 31000 | =SUMPRODUCT($B$3:$D$3,B4:D4) | ||
| Subject to: | LHS | RHS | ||||
| Sales Budget | 6000 | 11000 | 7000 | =SUMPRODUCT(B7:D7,$B$3:$D$3) | <= | 700000 |
| Total No. of SPs | 1 | 1 | 1 | =SUMPRODUCT(B8:D8,$B$3:$D$3) | <= | 100 |
| Min. SP in East | 1 | =SUMPRODUCT(B8:D8,$B$3:$D$3) | >= | 10 | ||
| Min. SP in Midwest | 1 | =SUMPRODUCT(B9:D9,$B$3:$D$3) | >= | 10 | ||
| Min. SP in West | 1 | =SUMPRODUCT(B10:D10,$B$3:$D$3) | >= | 10 |
Optimal Solution:
| Region | East | Midwest | West |
| No. of Salesperson | 12 | 10 | 74 |
| Total Sales Volume | 2,774,000 Units | ||
Part b: To the East region 12 salesperson are to assigned.
