Question

An office supply company needs to hire temporary workers to get through a busy season. They have two agencies to choose from: Temporary Solutions, and Tempo Temporary. A worker from Temporary Solutions can do 4 jobs per day, while a worker from Tempo Temporary can do 3 jobs per day, and the daily cost for one worker is $130 from Temporary Solutions and $100 from Tempo Temporary. If the office supply company needs enough temporary workers to do at least 30 jobs per day, and they must hire at least twice as many workers from Tempo Temporary as they hire from Temporary Solutions, how many workers should they hire to minimize the cost? Number of workers from Temporary Solutions: Number of workers from Tempo Temporary: Minimum daily cost in dollars:

Answer 1

Let the number of workers from temporary Solutions be X and that from Tempo Temporary be Y.

Then the constraints we are given here are:

The critical points for this region are computed as:

For Y = 2X,
4X + 3*2X = 30
X = 3 and Y = 6
C = 130X + 100Y = 130*3 + 100*6 = 990

For X = 0, Y = 10, C = 100*10 = 1000
For Y = 0, X = 7.5, but we cannot have decimal workers, therefore X = 8, C = 130*8 = 1040

Therefore to minimize cost, the correct critical point here is given as: X = 3 and Y = 6.

Number of workers from Temporary Solutions: 3
Number of workers from Tempo Temporary: 6
Minimum daily cost in dollars: 990