University:
Santa Ana College
Course:
MATH 150 | Calculus for Biological, Management and Social Sciences
Academic year:

2023
Views:

459

Pages:

2
Author:

lankstoetp7

Related Rates Math 150 Name:________________________________________________ Implicit Differentiation: 1) Suppose the VeeCam Company determines that the price-demand equation for their economy tripod is given by: p  2xp  x 2 125 where x represents the demand for tripods in thousands and dp p represents the price in dollars. Determine . Evaluate and interpret dp/dx at (2.5,19.5). dx  Related Rates: 2) Past records of the TechTop Company determine that the revenue for the number of software suites produced and sold is given by: R  90x  x 2 , where x is the units produced and sold and R is the revenue in dollars. The company also finds that the software is selling at a rate of 5 suites per day. How fast is the revenue changing when 40 suites are being produced and sold?  3) The SoftSkirt Company determines that the monthly revenue for a new style skirt is given by: 1 R  60  x 2 , where x is the number of skirts produced and sold in hundreds, and R is the 2 revenue in thousands of dollars. Determine the rate of change in the revenue with respect to time at a production level of x = 3 and production increasing by 20 hundred skirts per month. 4) When the price of a certain commodity is p dollars per unit, the manufacturer is willing to supply x thousand units where, x 2  2x p  p2  31 How fast is the supply changing when the price is $9 per unit and is increasing at the rate of 20 cents per week? 5) When the price of a certain commodity is p dollars per unit, consumers demand x hundred units where 75x 2 17p2  5300 . How fast is the demand changing with respect to time when the price is $7 and is decreasing at a rate of 75 cents per month.  Answers: dp 2x  2 p , when the demand is 2.5 thousand tripods and the price is $19.50, the price is  dx 1 2x decreasing at a rate of $7.33 per thousand tripods 1) 2) Revenue is increasing at a rate of $50/day, when 40 suites are produced and sold. 3) When 300 skirts are sold and increasing by 2000/month, the revenue is decreasing at a rate of $60,000/month, 4) The supply is increasing at a rate of 206 units/week (you must use x =14) 5) The demand is increasing approx 15 units/month (use dp/dt = -0.75)

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