SOLUTION: An Office Supply company sells x permanent markers per year @ $ p per marker. The price demand equation for these markers is: P = 10-0.0001x The total annual cost of manufact

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Question 1035400: An Office Supply company sells x permanent markers per year @ $ p per marker.
The price demand equation for these markers is: P = 10-0.0001x
The total annual cost of manufacturing X permanent markers for the office supply company is: C(x) = 5000 + 2x
What is the company's maximum profit?
What should the company charge for each permanent marker?
How many markers should the company produce?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The total revenues would be
R%28x%29+=+x%2810-0.0001x%29
==> Total profits would be P%28x%29+=+R%28x%29+-+C%28x%29+=+-010x+-+5000+-+2x+=+-0.0001x%5E2+%2B+8x+-5000
To maximize profits, the company should produce x+=+-b%2F%282a%29+=+-8%2F%282%2A-0.0001%29 = 40,000 markers.
The company should charge 10 - 0.0001*40,000 = $6 for each marker.
The company's maximum profit is P%2840000%29+=+-0.0001%2A40000%5E2+%2B+8%2A40000+-5000+ = $155,000.