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I Like Pi

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## Homework Statement

The problem goes like this:

A man is selling two types of lightbulbs. Lightbulb X costs $1.70, but 9% are defective, and so, cannot be sold. Lightbulb Y costs $0.90, but 12% are defective. The man wants to purchase at least 10 000 lightbulbs of each type, but he wants at least 10% of the total to be lightbulb X and at most 70% of total of lightbulb Y. Minimize the total cost.

**I believe they are constraints, but have no clue how... And please, do not give me the answer, i would like to learn.**

__Now my question is what do I do with the defect rates?__Thank you in advance,

I like Pi

## Homework Equations

## The Attempt at a Solution

I have:

Let x = # of X lightbulbs

Let y = # of Y lightbulbs

C

_{min}= 1.7x + .9y (objective)

constraints:

x, y ≥ 10 000

x ≥ .10(x+y) ... x ≥ (.10/.90)y

y ≤ .70(x+y) ... y ≤ (.70/.30)x