A manufacturer produces two models of toy airplanes. It takes the manufacturer20minutes to assemble model A and10minutes to package it. It takes the manufacturer15minutes to assemble model B and12minutes to package it. In a given week, the total available time for assembling is1800minutes, and the total available time for packaging is1080minutes. Model A earns a profit of$12for each unit sold and model B earns a profit of$8for 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?

Question
Asked Nov 4, 2019
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A manufacturer produces two models of toy airplanes. It takes the manufacturer

20

minutes to assemble model A and

10

minutes to package it. It takes the manufacturer

15

minutes to assemble model B and

12

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

1800

minutes, and the total available time for packaging is

1080

minutes. Model A earns a profit of

$12

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?

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Expert Answer

Step 1

To find: The number of units of two model (i.e.) A & B.

Let x be the number of toy airplane of Model A and Let y be the number of toy airplane of Model B.

Given data provided in table,

Assemble
Package (min)
Profit
(min)
Model A (x)
Model B (y)
Weekly
production (Min)
$8
20
10
$12
15
12
1800
1080
help_outline

Image Transcriptionclose

Assemble Package (min) Profit (min) Model A (x) Model B (y) Weekly production (Min) $8 20 10 $12 15 12 1800 1080

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Step 2

The constraints is written from the table is,

20x 151800
10x +12y180
x20; y20
help_outline

Image Transcriptionclose

20x 151800 10x +12y180 x20; y20

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Step 3

The objective function...

The profit of the manufacture is,
Z=8x +12y
help_outline

Image Transcriptionclose

The profit of the manufacture is, Z=8x +12y

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Math

Algebra

Linear Programming