An office supply company sells x permanent markers per year at p dollars per marker. The price-demand equation for these markers is p=10-0.001x. The total annual cost of manufacturing x permanent markers for the office supply company is C(x)=5000+2x. a) What price should the company charge for the markers to maximize revenue? What is the maximum revenue? Price: Maximum Revenue: b) What is the company's maximum profit? What should the company charge for each marker and how many markers should be produced? Maximum Profit: Marker Price: Markers Produced: c) The government decides to tax companies $2 for each maker produced. Taking into account this additional cost, how many markers should the company manufacture annually to maximize its profit? What is the maximum profit? How much should the company charge for the markers to realize the maximum profit? Markers Priduced: Maximum Profit: Marker Price:
I asked this question yesterday and I don't understand why somebody did a) Demand: p=100-0.001x when p is 10, not 100?
1. An office supply company sells x permanent markers per year at p dollars per marker. The price-demand equation for these markers is p=10-0.001x. The total annual cost of manufacturing x permanent markers for the office supply company is C(x)=5000+2x.
a) What price should the company charge for the markers to maximize revenue? What is the maximum revenue?
Price:
Maximum Revenue:
b) What is the company's maximum profit? What should the company charge for each marker and how many markers should be produced?
Maximum Profit:
Marker Price:
Markers Produced:
c) The government decides to tax companies $2 for each maker produced. Taking into account this additional cost, how many markers should the company manufacture annually to maximize its profit? What is the maximum profit? How much should the company charge for the markers to realize the maximum profit?
Markers Priduced:
Maximum Profit:
Marker Price:
Expert Answer
a) Demand : p=100-0.001x
Cost : C(x)=5000+2x
Revenue=Price * Quantity
So, R = px
To maximize revenue, we will take first-order conditions and equate the expression to zero.
R=(100-0.001x)x
R=100x-0.001x2
dR/dx=100-0.002x
100-0.002x=0
0.002x=100
x=100/0.002
x=50,000
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