Question

The total revenue function for two goods is given by the equation TR = 36 x-3x²+ 56y- 4y².find the number of unit of each goods which must be sold. if profit is to be maximize when the firm subject to a budget constraint 5 x + 10 y = 80

Answer 1

$TR=36x+3x²+56y-4y²$

Budget constant $5y+10y=80$

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

$TR=36(16-2y)+3(16-2y)²+56y-4y²$

$\frac{∆TR}{∆Y}=-72y+6(16-2y)+56+8y$

$\frac{∆TR}{∆Y}=-104y+248=0$

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

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

$y=2.385\\x=11.231$