(a) DEMAND RATE When the price of a certain commodity is p dollars per unit, customers demand at hundred units of the commodity, where 12+3pr+p1=?9. How fast is the demand at changing with respect to time when the price is $5 per unit and is decreasing at the rate of 30 cents per month? (1:) MANUFACTURING At a certain factory, output Q is related to inputs a and s by the equation 2:: + 3:: _ 2 {2311 +W. If the current levels of input are u = 10 and a = 25, use calculus to estimate the change in input u that should be made to offset a decrease of EL? unit in input I: 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 1' hundred units, where 3p1x2=12. How fast is the supply changing when the price is $4 per unit and is increasing at the rate of 3? cents per month? (d) MANUFACTURING At a certain factory, output Q is related to inputs :r and y by the equation Q =2x3+3x=y2+(1+y)2. If the current levels of input are r = 30 and y = 2n, use calculus to estimate the change in input 3! that should be made to offset a decrease of [LB unit in input at so that output will be maintained at its current level