Question

8. A carpenter balances his daily projects between small jobs (x) and building cabinets (y). He allots 2
hours per small job and 4 hours per cabinet job. He works at most 12 hours per day (2x + 4y <_12).
He cannot do more than 3 small jobs per day
and get all of his cabinets done (Y >_0) & (0 The carpenter earns $125 per small job and $500 per cabinet job. Find a combination of small jobs and
completed cabinet jobs per week that will maximize income.

Answer 1

Answer:

$\ 1125$

Step-by-step explanation:

The equations of the system are

$2x+4y\leq 12$

$y\geq 0$

$0<x\leq 3$

From the graph it can be seen that points $(3,1.5)$ and $(3,0)$ falls in the bounded region.

The income will be

$125x+500y=125\times 3+500\times 1.5\\ =\ 1125$

$125\times 3+500\times 0=\ 375$

So, the person can do 3 small jobs and build 1 and a half cabinets per day.

The maximum income will be $\ 1125$.