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.