Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Question

Chapter 10.2, Problem 57E

(a)

To determine

To find: The number of cases of each drug should be produced in order to maximize profit, if the company makes a profit of $320 on each case of drug A and $500 on each case of drug B.

(a)

Expert Solution

Answer to Problem 57E

5 cases of drug A and 8 cases of drug B

Explanation of Solution

Given information: Business: A pharmaceutical company manufactures two drugs. Each case of drug A requires 3 hours of processing time and 1 hour of curing time per week. Each case of drug B requires 5 hours of processing time and 5 hours of curing time per week. The schedule allows 55 hours of processing time and 45 hours of curing time weekly. The company must produce no more than 10 cases of drug A and no more than 9 cases of drug B.

Calculation:

Lots of information here, starting from the end sometimes helps identify the variables.

We are maximizing profit: P=320x+500y

Where x is amount of drug A cases and y is the amount of drug B cases

We know that 3(p)rocessing hours + 1(c)uring hour = drug A

So, 3p+c are for drug A.

We know that 5p+5c for drug B.

The problem says a maximum of 55 hours processing and 45 hours of curing are mandated.

Take the processing hours from each and set ≤55:3x+5y≤55

Take the curing hours from each and set ≤45:x+5y≤45

Finally we know that,

drug A≤10→x≤10

drug B≤9→y≤9

Graphing these inequalities you get:

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.2, Problem 57E

Test each vertex: (you don’t have to test (0,0) )

(0,9)=320(0)+500(9)=4500(5,8)=320(5)+500(8)=5750 max(10,5)=320(10)+500(5)=5700(10,0)=320(10)+500(0)=3200

The company should produce 5 cases of drug A and 8 cases of drug B.

(b)

To determine

To find: The maximum profit.

(b)

Expert Solution

Answer to Problem 57E

5750 dollars

Explanation of Solution

Calculation:

(5,8)=320(5)+500(8)=5750

Thus,

The maximum profit is 5750 dollars.

Chapter 10.2, Problem 56E

Chapter 10.2, Problem 58E

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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