Partial preview of the text
Download Calculus for Business - Worksheet Problems | MATH 165 and more Assignments Calculus in PDF only on Docsity!
| math16504.mw Maple 9.5 Worksheet for Problems in Math 165 - Calculus for Business. First load plots and student: _> restart:with( student) :with (plots): Chapter 2 Section 2.1 Problem 37. p. 111 PROFIT A manufacturer can produce tape recorders at a cost of 20 dollars apiece. It is estimated that if the tape recorders are sold for p dollars apiece, consumers will buy q = 120 - p recorders each month. (a) Express the manufacturer's profit as a function of q. (b) What is the average rate of profit obtained as the level of production increases from q=0toq=20? (c) At what rate is the profit changing when q = 20 recorders are produced? Is the profit increasing or decreasing at this level of production? To answer (a), Profit(q) = Revenue(q) - Cost(q), Revenue(q) = (quantity) x (price) = q p = q *(120 - q), Cost(q) = 20*(q), Since Cost/item is constant = 20, an alternate expression is Cost(q) = (p - 20) q = 100 -q. > Revenue:= proc(q) description Revenue at price q’; > q*(120 - q): > end proc; Revenue (q) ; Revenue := proc(q) description Revenue at price q; q * (120—q) end proce q (120-9) > Cost:= proc(q) description*Cost at price q*; > 20 * q: > end proc;Cost(q) ; > Cost = proc(q) description Cost at price g, 20* g end proc 204 > Profit:= proc(q) description’ Profit at price q’; > Revenue (q) - Cost(q): > end proc;Profit(q) ; Profit = proc(q) description Profit at price g, Revenue(q) —Cost(q) end proc q (120-q) -20 q > simplify ([Revenue(q) ,Cost(q) ,Profit(q)]); [-g (-120 +g), 20g, 100 g-q"] 
