$1.$ In problem $2,$ if the price of the standard$-$mix package remains the same but the price of deluxe$-$mix

packages changes to $$3,$ what would have been the vertex that maximizes revenue? What would be the

maximum revenue?

$2.$ In problem $3,$ if the price of the standard phone remains the same but the price of the deluxe phone

changes to $$80,$ which vertex would maximize the revenue? What would be the maximum revenue?

$3.$ Do you think that real life problems often have challenging constraints? Do you think that real life

problems are always easy to solve, or do you think that many involve sitting down and working

patiently through mathematical computations? In a few short sentences explain your thoughts on these

questions.

$4.$ Problem $2$ and Problem $3$ had very different premises. However, from a mathematical perspective, do

you believe they are similar? Do you believe that there may be many $$real life$$ scenarios which appear

very different on the surface, but which through the language of mathematics become similar? In a few

short sentences, explain your thoughts on these questions.