The president of a Supermarket plans to hire two marketing f

The president of a Supermarket plans to hire two marketing firms to survey 500 customers by phone, 750 by mail, and 250 by in-person interviews. Gareia Researeh has personnel to do 10 phone surveys, 30 mail surveys and 5 interviews in each hour for which they are contracted. Wong Marketing can handle 20 phone surveys, 10 mail surveys and 10 interviews per hour. For how many hours should each of these firms be contracted to produce the exact number of surveys needed, assuming their hourly costs are equal?

Solution

If G and W are the number of hours contracted to the firms , then

                                10G+ 20W=500..........................(1)

                                 30G+10W=750..........................(2)

                                 5G+10W=250.............................(3)

(2)-(3) gives G=20 hours, and W= 15 hours and these values satisfy (1) as well