Question

Problem Page

A manufacturer produces two models of toy airplanes. It takes the manufacturer
32

minutes to assemble model A and
8

minutes to package it. It takes the manufacturer
20

minutes to assemble model B and
10

minutes to package it. In a given week, the total available time for assembling is
3200

minutes, and the total available time for packaging is
960

minutes. Model A earns a profit of
 

$
10

 

for each unit sold and model B earns a profit of
 

$
8

 

for each unit sold. Assuming the manufacturer is able to sell as many models as it makes, how many units of each model should be produced to maximize the profit for the given week?

Note that the ALEKS graphing calculator can be used to make computations easier.


Model
A:
unit(s)
Model
B:
unit(s)

Answer 1

Company A:
Assembling: 3200 mins /32 mins per toy=100 toys
Packaging: 960 mins / 8 mins per toy= 120 toys

Company B:
Assembling: 3200 mins / 20 mins per toy= 160 toys
Packaging: 960 mins / 10 mins per toy= 96 toys

Answer 2

A=80units for model A

B=32units for model B

Explanation:

We take A as the quantity produced for model A and B as the quantity for model B.

the total available time for assembling is

3200

the total available time for packaging is

960

Therefore 32A+20B≤3200

8A+10B≤960

we will arrive at maximum production when all the units are used up

32A+20B=3200 assembling time

8A+10B=960 packaging minutes

solving the sumultaneius equation using substitution method

from equation 1

B=(3200-32A)/20

B=160-1.6A

substitute B into equation 2

8A+10(160-1.6A)=960

8A=640

A=80

from equation 2

8A+10B=960

8(80)+10B=960

B=32