Question

A sales representative covers territory in iowa and kansas. her daily travel expenses average $120 in iowa and $100 in kansas. her company provides an annual travel allowance of $18; 000. her company also stipulates that she must spend at least 50 days in iowa, and 60 days in kansas per year. if sales average $3; 000 per day in iowa, and $2; 500 per day in kansas, how many days should she spend in each state to maximize sales?

Answer 1

To maximize sales, the sales representative should spend 50 days in Iowa and 60 days in Kansas. The total sales in each state should be calculated after deducting the travel expenses, and the remaining travel allowance should be distributed proportionally.

Step-by-step explanation:

To maximize sales, the sales representative should spend 50 days in Iowa and 60 days in Kansas. Here's the step-by-step explanation:

1. Calculate the total travel expenses in each state: $120 x 50 = $6000 in Iowa and $100 x 60 = $6000 in Kansas.
2. Calculate the total sales in each state: $3000 x 50 = $150000 in Iowa and $2500 x 60 = $150000 in Kansas.
3. Calculate the remaining travel allowance after deducting the expenses: $18000 - $6000 - $6000 = $6000.
4. Distribute the remaining travel allowance proportionally to the number of days spent in each state. For Iowa: $6000 x (50/110) = $2727.27 and for Kansas: $6000 x (60/110) = $3272.73.
5. Add the additional travel allowance to the sales in each state: $150000 + $2727.27 = $152727.27 in Iowa and $150000 + $3272.73 = $153272.73 in Kansas.

Therefore, the sales representative should spend 50 days in Iowa and 60 days in Kansas to maximize sales.