SOLUTION: Hi, please help me solve this. Thank you! Linear Programming Application (1) An office manager needs to staff the office. She hires full-time employees at $18 per hour and pa

Algebra ->  Inequalities -> SOLUTION: Hi, please help me solve this. Thank you! Linear Programming Application (1) An office manager needs to staff the office. She hires full-time employees at $18 per hour and pa      Log On


   

Question 1061768: Hi, please help me solve this. Thank you!
Linear Programming Application
(1) An office manager needs to staff the office. She hires full-time employees at $18 per hour and part-time employees at $12 per hour. Write an objective function that represents the total cost (in $) to staff the office with x full-time employees and y part-time employees for 1 hr.

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(2) Refer to 1. Suppose that the office manager needs at least 20 employees, but not more than 24 full-time employees. Furthermore, to make the office run smoothly, the manager knows that the number of full-time employees must always be greater than or equal to the number of part-time employees. Write a system of inequalities that represents the constraints on the number of full-time employees x and the number of part-time employees y.
Found 2 solutions by KMST, ikleyn:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= number of full-time employees
y= number of part-time employees
The objective function is
C=18x%2B12y .

"At least 20 employees" means x%2By%3E=20 .
"No more than 24 full-time employees" means x%3C=24
"The number of full-time employees must always be greater than or equal to the number of part-time employees" means x%3E=y or y%3C=x .

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
The additional constraints are x >= 0, y >= 0.