A chain saw requires 7 hours of assembly and a wood chipper 4 hours. A maximum of 84 hours of assembly time is available. The profit is $160 on a chain saw and $ 220 on a chipper. How many of each should be assembled for maximum profit?

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AlonsoDehner AlonsoDehner · Answer 1 · 2019-12-07T13:52:31+01:00

Answer:

0 and 21.

Step-by-step explanation:

Given that a chain saw requires 7 hours of assembly and a wood chipper 4 hours. A maximum of 84 hours of assembly time is available.

Let X be the number of chain saw and Y no of chippers.

Then constraint is

total no of hours =84

i.e. [tex]7x+4y\leq 84[/tex]

Our objective is to maximize total profit

[tex]z=160x+220y[/tex]

We find that y fetches more profit

So total 84 hours if utilized for y, we can manufacture 21 with total profit

[tex]21 *220 = 4840[/tex]

Instead if 12 units of chain saw produced profit would be 160(12) = 1820

very less than the amount 4840

So 21 units of chipper and no chain saw should be assembled.