Please take the time to explain and over explain, I have answers and have been able to come up with solutions but would like to see things mathmatically/clearly

Question 1 (Customers)

Monique is a music professor who has been tasked to purchase upright pianos for her music conservatory. She is evaluating three competing piano models on 4 attributes. Her dollar valuations for each of those 4 attributes for all three piano models are listed below. Her overall valuation for each piano model is the sum of the valuations of all the 4 attributes.

	Yamaha U1	Boston 48	Kawai K5
Sound Quality	$4000	$3800	$3600
Reliability	$3000	$2000	$3200
Brand	$1000	$900	$500
Warranty	$0	$500	$1000

The price of each piano model that Monique was quoted are given below

	Yamaha U1	Boston 48	Kawai K5
Price	$6800	$7100	$6900

Based on the valuations above, how much more would Monique be willing to pay for a Yamaha U1 compared to a Boston 48? ($800)

Between the Yamaha U1 and the Kawai K5, which piano model would Monique choose? (Kawai K5)

Suppose you are the manager for the Boston 48. By how much must you lower your price to ensure that Monique will choose your piano? ($1301)