Question

A retail catalog store specializes in outdoor clothing. Phone orders are taken each day by a large pool of computer operators, some of whom are permanent and some temporary. A permanent operator can process an average of 90 orders per day, whereas a temporary operator can process an average of 60 orders per day. The company averages at least 800 orders per day. The store has 11 computer workstations. A permanent operator is paid $150 per day, including benefits, and a temporary operator is paid $100 per day. Determine the number of permanent and temporary operators to hire to minimize costs.

Answer 1

5 permanent operators and 7 temporary operators

Step-by-step explanation:

Let x represent the number of permanent operators and y represent the number of temporary operators.

The objective function is given as:

Minimize cost = 150x + 100y

There are 11 computer stations, hence:

x + y = 11 (1)

Also since the company averages at least 800 orders per day:

90x + 60y ≥ 800 (2)

The solution to the problem gives (11,0), (13.33, 0), (4.67, 6.33)

At (11, 0), Minimize cost = 150(11) + 100(0) = $1650

At (13.33, 0) , Minimize cost = 150(14) + 100(0) = $2000

At (4.67, 6.33), Minimize cost = 150(4.67) + 100(6.33) = $1334

The minimum cost is at x = 4.67 ≈ 5 and y = 6.33 ≈ 7

To minimize cost there is need to have 5 permanent operators and 7 temporary operators