Question

the total revenue function for the two goods is given by the equation; TR=36x+3x²+56y-4y². Find the number of units of each good which must be sold if profit is to be maximised when the firm is subject to a budget constraint, 5y+10y=80. I am look for the solution to this problem

Answer 1

Given

$TR=36x+3x²+56y-4y²$

Budget constant $5y+10y=80$

$x+2y=16\\x=16-2y$

$TR=36(16-2y)+3(16-2y)²+56y-4y²$

$\frac{∆TR}{∆Y}=-72y+6(16-2y)+56+8y$

$\frac{∆TR}{∆Y}=-104y+248=0$

$Y=\frac{248}{104}$

$x=16-\frac{496}{104}=\frac{1168}{104}$

$y=2.385\\x=11.231$