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Homework answers / question archive / 1) A coal power plant in Michigan uses coal ash and co-fires it with biofuels in the production of electricity
1) A coal power plant in Michigan uses coal ash and co-fires it with biofuels in the production of electricity. The cost Y, expressed as thousands of dollars per hour, to produce electricity is Y = 20 + X + 0.15X2, where X is in megawatts. Revenue in thousands of dollars per hour from the sale of electricity is expressed as 25X−0.5X2. Find the value of X that produces the maximum profit for the plant. Submit your answer to the nearest hundredth of a megawatt
2) The manufacturer of Brand A automobile tires claims that its tire can save 110 gallons of fuel over 55,000 miles of driving, as compared to a popular compeditor (brand B). If gasoline costs $4.00 per gallon, how much per mile driven does this tire save the customer (Brand A versus Brand B)?
Answer:
1) TC =
Y= 20+X+0.15X²
MC= 1+0.30X
TR=
25X-0.5X²
MR= 25-1X
For maximum profit, MR=MC
25-1X = 1+0.30X
24= 1.30X
X= 2400/130 = 18.46 ~18 megawatt.
2)
total fuel save = 110 gallons
Miles covered = 55000 ,
Total saving = 110*4 = $440
so saving per mile = 440 / 55000 = $ .008 per mile
