Answer to Question #118623 in Microeconomics for mehenuz

Question

q=500-0.5p and AC=q^2-59q+1315+200/q find the level of output and price at which profit will be maximized. find MC x=5 and interpret

Answer 1

$Pr=TR-TC$

$TR=p\times q$

$TC=AC\times q$

$p=1000-2q$

$TR=1000q-2q^2$

$TC=q^3-59q^2+1315q+200$

$Pr=1000q-2q^2-q^3+59q^2-1315q-200$

$Pr=-q^3+57q^2-315q-200$

$Pr^/=-3q^2+114q-315$

$-3q^2+114q-315=0$

$q^2-38q+105=0$

$q=35 or q=3$

q=3 is maximum point of function

$p=1000-2\times 3=994$

$MC=TC^/$

$MC=3q^2-118q+1315$

$3q^2-118q+1315=3\times5^2-118\times5+1315=75-590+1315=800$

Under the given conditions, the maximum profit will not be.