Question

National Business Machines manufactures x model A fax machines and y model B fax machines. Each model A costs $100 to make, and each model B costs $150. The profits are $35 for each model A and $30 for each model B fax machine. If the total number of fax machines demanded per month does not exceed 2500 and the company has earmarked no more than $600,000/month for manufacturing costs, how many units of each model should National make each month to maximize its monthly profit?

(x, y)

=

What is the optimal profit?
$

Answer 1

Total production limit per month 2500

Now we see that,

150*2500 = 375000, that means even if all B are made, still the limit of 600000/month cannot be reached.

So we can have the relation between x and y as,

y = 2500 - x

Profit is given as:

P = 35x + 30y

Replacing y we get,

P = 35x + 30(2500 - x)

P = 35x + 75000 - 30x

P = 75,000 - 5x

As this is a linear equation, maximum will occur at end-points:

Either at x=0 or x=2500

From equation of P, we can see maximum occuring at x=0.

Since we have, y = 2500 - x,

then y = 2500

Then we get (x,y) as (0,2500)

And, P = 75000 - 5(0) = 75000

Optimal profit = $75,000