A company makes two product, A and B. the managers estimated that if x% of the t

Question

A company makes two product, A and B. the managers estimated that if x% of the total marketing budget is spent on marketing product A, then the total profit gained from both product will be P thousand dollars, where

{36 + 0.5x for 0 x < 30

{33 + 0.6x for 30 x <60

{84 – 0.25x     for 60 x 100

Previous 12 3 4 5 6 7 Next 1.4 Section Exercise 22 Question 1 of 7 (1 point) View problem in a pop-up A company makes two products, A and B. The manager estimates that if x % of the total marketing budget s spent on marketethe fotprott ained from botn uestion Check Answer products will be P thousand dollars, where Link to Textbook 36 +0.5x for 0sx

Explanation / Answer

Solution:

If x% of the total budget is spent on product A and y% of the total budget is spent on product B, then x% + y% = 100%. So we can replace x with 100 - y. Thus, P is given by:

{ 36 + 0.5(100 - y) for 0 (100 - y) < 30
{ 33 + 0.6(100 - y) for 30 (100 - y) < 60
{ 84 - 0.25(100 - y) for 60 (100 - y) < 100

which is equivalent to:

{ 36 + (50 - 0.5y) for -100 -y < -70 <--[Subtract 100 from each term in inequality.]
{ 33 + (60 - 0.6y) for -70 -y < -40
{ 84 + (-25 + 0.25y) for -40 -y < 0

which is equivalent to:

{ 86 - 0.5y for 100 y > 70 <--[Multiply each term by -1 and flip the inequality.]
{ 93 - 0.6y for 70 y > 40
{ 59 + 0.25y for 40 y > 0

which is equivalent to:

{ 86 - 0.5y for 70 < y 100 <--[Reverse the order of terms in the inequality.]
{ 93 - 0.6y for 40 < y 70
{ 59 + 0.25y for 0 < y 40

which is equivalent to:

{ 59 + 0.25y for 0 < y 40 <--[Sort each piece into increasing order.]
{ 93 - 0.6y for 40 < y 70
{ 86 - 0.5y for 70 < y 100

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