Bring the lp to standard form. (b) suppose the objective function changes to max z = 2x1−5x2+ 6x3. how does the standard form of (a) change? (c) suppose the first constraint changes to 3x1 + 7x2 + x3 ≤ −1. how does the standard form of (a) change? (d) consider a general lp with m constraints and n variables. how many basic solutions can an lp have? (this should be some formula in m and n). (e) how many basic solutions can the above lp have at most?

Step-by-step explanation:

always remember some basic principles when dealing with percentages :

100% is the whole

1% = 100%/100

n% = n×1% = n×100%/100

therefore, n% of an amount m is n/100 × m.

like 25% = 25/100 × m = 0.25 × m

so, now it should be very easy :

the 25% discount of $80 is

0.25×80

the amount deducted by (= after) the discount is

80 - 0.25×80

which is actually 0.75×80

a markup is added into the total cost incurred by the producer of a good or service in order to cover the costs of doing business and create a profit. so, a markup of 40% is simply again

0.40×80

and the sale price including (= after) the markup is then

80 + 0.40×80