Suppose that you own the Newton Publishing Inc. (NPI) that sells textbooks in se

Question

Suppose that you own the Newton Publishing Inc. (NPI) that sells textbooks in seven Southern states. The sales region is shown below with states, A through G, and the number of students (in thousands) located in each state. Each sales rep must cover two adjacent states. Answer the following questions 21 18 21 42 56 29 34 a. Suppose that you want to assign the minimum number of sales reps so as to guarantee that each state is covered by at least one sales rep. What would be the minimum number of sales reps needed? Please show your work. b. Now ignore your answer in part (a). Suppose you only have one sales rep, and vou want to use this rep to maximize the student count covered. Please calculate the maximum number of students vou can cover. Please show vour work c. Suppose you have two sales reps, and you want to use them to maximize the student count covered. No state can have more than one rep. Please calculate the maximum number of students you can cover. Compute how many more students are covered due to this one more sales rep compared to part (b) d. Suppose you have one more sales rep, i.e., you have three sales reps now, and you want to use them to maximize the student count covered, No state can have more than one rep. Please calculate the maximum number of students you can cover, and compute how many more students are covered due to this one more sales rep compared to part (c) e. Based on your answers above, calculate the value of adding one more sales rep in terms of the additional number of students you can cover, given that you have the number of sales reps (denoted as N), when N-0, 1, 2, 3, 4, 5. This notion is similar to the "shadow price" in linear programming Layout of Answer . o Please create one answer sheet within vour excel solution for all parts

Explanation / Answer

Let us Arrange the total number of students count in desending order forl all states:

a) Minimum number of sales rep as each state must have atleast one sales rep

It is given that a sales rep covers 2 adjacent states,

Thus total sales rep needed = (No. of states)/2 = 7/2 = 3.5

Thus minimum sales rep needed is 4 ( Sales rep cannot be in decimal)

b) Suppose we have ony 1 sales rep.

Now we know that a sales rep can cover two adjacent states.

Thus we will go by states with highest students and one adjacent state with nect highest student

The states with highest students is E i.e. 56 and its adjacent state with highest student is state B i.e. 29

Total students covered = 56+29 = 85

Thus, maximum students covered is 85

c) Now we have two more sales rep, so we can now cover 2 more adjacent states

As we calculates in part b. the states covered are E and B and students covered are 85

Now states left to cover are state A,C,D,F and G

The adjacent states with highest students are States i.e. 34 and State C i.e. 42

Thus total Students covered in states A and C is 76

Thus total students covered in state A , B , C and E is 161 students

Increase from part B is 161- 85 = 76 students

d) Now we have one more sales rep, thus total we have three sales rep

Now states left to cover are: D , F and G

States with highest Students is G and D i.e. 21 and both states are adjecent

Thus, we will cover states G and D ,

So total students covered by new sales rep is 21 + 21 = 42

So total students covered in states A, B, C , D, E AND G = 34+ 29 + 42 + 21 + 56 + 21 = 203 students

Increase from part c is 203 - 161 = 42 students

e) Value of adding one more sales rep.

State Students E 56 C 42 A 34 B 29 D 21 G 21 F 18

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