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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 25 minutes to assemble model B and 5 minutes to package it. In a given week, the total available time for assembling is 3000 minutes, and the total available time for packaging is 1200 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?

Sagot :

boffeemadrid

Answer:

[tex]\$1320[/tex]

Step-by-step explanation:

Let [tex]x[/tex] be the number of units of A

[tex]y[/tex] be the number of units of B

For assembling we have

[tex]20x+25y\leq 3000[/tex]

For packaging we have

[tex]10x+5y\leq 1200[/tex]

Let profits earned be [tex]Z[/tex] so

[tex]Z=10x+8y[/tex]

We have the maximize the function.

Plotting the equations we can see that the intersection points are [tex](0,120),(100,40),(120,0)[/tex]

In the question it is mentioned we have to sell both the products so [tex]x[/tex] or [tex]y[/tex] cannot be [tex]0[/tex].

So, the point of maximiztion for the function would be [tex](100,40)[/tex]

The maximum profit would be

[tex]Z=10\times 100+8\times 40\\\Rightarrow Z=1320[/tex]

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