Anton had started a cafe that sells coffee and tea. He has to decide what price to sell coffee and tea at. Let x be the quantity of coffee sold, and let y be the quantity of tea sold. Also, letPxbe the price per unit of coffee, and letPybe the price per unit of tea. The demand functions for coffee and tea are respectively:

Px=602xy

Py=40-2y-x

Each unit of coffee costs $2 for Anton to produce, and each unit of tea costs $2 for Anton to produce.

a. Suppose Anton chooses pricesPxandPto maximize his net profit (revenues minus costs). What quantities of coffee and tea (x and y) will he sell?

x =

y =

b. Suppose the cost per unit of coffee decreases by one percent, from $2 to $1.98. Anton adjusts his prices accordingly to maximize his net profit. What will be the percentage changes in x and y, the quantity of coffee and tea that Anton sells?

what is the % change in x =

what is the % change in y =