SOLUTION: I'm just trying to figure out what formula I should be using for this question: A factory manager is working to write a schedule of hours for his 20 workers. Each individual works

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Question 889414: I'm just trying to figure out what formula I should be using for this question: A factory manager is working to write a schedule of hours for his 20 workers.
Each individual works a 40 hour work week. This particular factory makes two products (calculators and Personal Digital Assistants). If each hour worked on building calculators earns the factory $10 and each hour worked on building PDAs earns the factory $15, how many hours should be spent building calculators if the manager wants to earn a profit of $9000? What about $10000 or $20000? What should the factory manager decide if he wants to earn the maximum profit?
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
let x be the amount of hours building calculators and y be the amount of hours building PDA's. We know that the factory manager has 20 employees who work 40 hours a week which means he has 20*40 hours per week, that is 800 hours
our two formulas are
x + y = 800
10x +15y = profit
solve first equation for y
y = 800 -x
1) 10x +15y = 9000
substitute for y in second equation
10x +15(800-x) = 9000
10x +12000 -15x = 9000
-5x = -3000
x = 600
600 hours should be spent building calculators
2) 10x +12000 -15x = 10000
-5x = -2000
x = 400
400 hours should be spent building calculators
3) 10x +12000 -15x = 20000
-5x = 8000
x = -1600
can not make $20000 profit in a week
suppose we have 2 weeks to make $20000, then
10x + 15(1600-x) = 20000
10x +24000 - 15x = 20000
-5x = -4000
x = 800
400 hours should be spent building calculators each of the 2 weeks or a total of 800 hours
4) maximum profit per week means everybody makes PDA's
800 *15 = $12000 per week