Answer to Question #142617 in Microeconomics for Ben

Question

CARO Departmental stores sends sales reps to call on three kind of customers: Retail, Industrial and Professional. Sales revenue of $8,000 results from calling retail customer, $14,000 from calling Industrial customer and $20,000 from calling Professional customer. Each quarter a total of 3200hrs of sales reps time is available for calling on customer and $10,000 available on travelling expenses. Six hours of travel and selling are required to call on retail customer with $10 sales rep traveling expenses; 11hours for Industrial customer with $14 sales rep traveling expenses; and 25 hours for Professional customer with $25 sales rep traveling expenses. What is optimal customer mix for each quarter?

Answer 1

Let number of retail clients be $r$ , indurstrial

clients $i$ and professional $p$

Constraints are time $t \le 3200$ and cost $c \le 10,000$

The total time is shared as follows

$$6r+11i+25p \le 3200$$

The total cost is shared as follows

$$10r+14i+25p \le 10,000$$

Revenues are:

$$8,000r+14,000i+20,000p$$

Profits are the sum of revenue minus costs

$$(8,000r-10r) + (14,000i-14i)+(20,000p-25p)$$

$=(7,990r) + (13,986i)+(19,975p)$

The goal is to get the right mix of customers to maximize profits

Using Excel solver:

The optimal mix of customers that maximizes profits is 526 retail clients and 4 indurstrial clients.