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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?

Answer :

Answer:

A - 90 units

B = 0 units

Step-by-step explanation:

Here we have two models A and B with the following particulars

Model A B    (in minutes)

 

Assembly 20 15

Packing          10 12

Objective function to maxmize is the total profit

[tex]z=12A+8B[/tex] where A and B denote the number of units produced by corresponding models.

Constraints are

[tex]20A+15B\leq 1800\\\\10A+12B\leq 1080[/tex]

These equations would have solutions as positive only

Intersection of these would be at the point

i) (A,B) = (60,40)

Or if one model is made 0 then the points would be

ii) (A,B) = (90,0) oriii) (0, 90)

Let us calculate Z for these three points

A B Profit

60 40 1040

90 0 1080

0 90 720

So we find that optimum solution is

A -90 units and B = 0 units.

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