Homework SourseA company produces x units of commodity A and y units of com
A company produces x units of commodity A and y units of commodity B each hour. The company can sell all of its units when commodity A sells for p=25-8x dollars per unit and commodity B sells for q=90-10y dollars per unit. The cost (in dollars) of producing these units is given by the joint-cost function
C(x,y)=2xy+3 . How much of commodity A and commodity B should be sold in order to maximize profit?
Commodity A: units
Commodity B: units
C(x,y)=2xy+3 . How much of commodity A and commodity B should be sold in order to maximize profit?
Commodity A: units
Commodity B: units
Solution
profit z=(25-8x)x+(90-10y)y-(2xy+3) z=-8x^2-2xy+25x-10y^2+90y-3. to maximize z we set dz/dx=0 and dz/dy=0. so we get x=80/79=1.013 y=695/158=4.4 z=32801/158= 207.60
