Question: For a certain company, the cost function for producingx items isC(x)=30x+100 and the revenue function for sellingx items isR(x)=0.5(x110) 2 +6,050 . The maximum capacity

For a certain company, the cost function for producingx

items isC(x)=30x+100

and the revenue function for sellingx

items isR(x)=0.5(x110)

2

+6,050

. The maximum capacity of the company is150

items.

  1. What is the domain ofP(x)
  2. ?
  3. Hint: Does calculatingP(x)
  4. make sense whenx=10
  5. orx=1,000
  6. ?
  7. The company can choose to produce either80
  8. or90
  9. items. What is their profit for each case, and which level of production should they choose?
  10. Profit when producing80items =
  11. Profit when producing90items =
  12. Can you explain, from our model, whythe company makes less profitwhen producing 10 more units?

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