d & e (c) SUPPLY RATE When the price of a certain commodity is p dollars per unit, themanufacturer is willing to supply x hundred units, where3p? – x² = 12.How fast is the supply changing when the price is $4 per unit and is increasing atthe rate of 87 cents per month?(d) MANUFACTURING At a certain factory, output Q is related to inputs x and y bythe equationQ = 2r° + 3x*y? + (1+y)².If the current levels of input are x = 30 and y = 20, use calculus to estimate thechange in input y that should be made to offset a decrease of 0.8 unit in input x sothat output will be maintained at its current level. • For each item in this problem set, you will use the formula 1+ [(x+y) mod z),and the variables are specified therein. The result using the formula per item willcorrespond to the sub-item you will work on. Here, x is the number using lettersof the Filipino Alphabet where there are 28 of them; y comes your Student Number;and z is the number of the sub-items therein. Moreover, a mod b is the remainder bydividing a by b. Example: K is the 11th letter in the alphabet so x= 11 and supposey = 3, 2- 5. Hence,1+ [(x+y) mod z] =1+[(11+3) mod 5]= 1+[14 mod 5]= 1+4Therefore you solve the 5th sub-item, ie., (e).• Before you start writing or presenting your solution, be able to provide the values forX, y,z and computation using the formula above. This will be part of the assessment.Note your work will have no credit if- the computation using the formula is incorrect;- the set of values being asked is incorrect; oryou forget to put it.

Solution : C) rate =dydt 3p2-x2=12 …(1)⇒p=4⇒x2=3*16-12=36⇒x=6 rate of increasing of price = dpdt…

(c) SUPPLY RATE When the price of a certain commodity is p dollars per unit, the manufacturer is willing to supply x hundred units, where 3p? – x² = 12. How fast is the supply changing when the price is $4 per unit and is increasing at the rate of 87 cents per month? (d) MANUFACTURING At a certain factory, output Q is related to inputs x and y by the equation Q = 2r° + 3x*y² + (1 + y)². If the current levels of input are x = 30 and y = 20, use calculus to estimate the change in input y that should be made to offset a decrease of 0.8 unit in input x so that output will be maintained at its current level.

(c) SUPPLY RATE When the price of a certain commodity is p dollars per unit, the manufacturer is willing to supply x hundred units, where 3p? – x² = 12. How fast is the supply changing when the price is $4 per unit and is increasing at the rate of 87 cents per month? (d) MANUFACTURING At a certain factory, output Q is related to inputs x and y by the equation Q = 2r° + 3x*y² + (1 + y)². If the current levels of input are x = 30 and y = 20, use calculus to estimate the change in input y that should be made to offset a decrease of 0.8 unit in input x so that output will be maintained at its current level.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 18T

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