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=80-5x dollars per unit and commodity B sells for p=75-10y dollars per unit. The cost (in dollars) of producing these units is given by the joint-cost function C(x,y)=4xy+4. How much of commodity A and commodity B should be sold in order to maximize profit?
Commodity A: units
Commodity B: units
Commodity A: units
Commodity B: units
Solution
profit z=(80-5x)x+(75-10y)y-(4xy+4) z=-5x^2-4xy+80x-10y^2+75y-4 to maximize z dx/dx=0 dz/dy=0 so we get x=325/46,y=215/92 and z=67389/184
