Roger's Lobsters serves buy-by-the-pound lobster dinners every Monday night. In order to attract customers, Roger's can take out radio ads on local...

1.Roger's Lobsters serves buy-by-the-pound lobster dinners every Monday night. In order to attract customers, Roger's can take out radio ads on local radio stations. If Roger's buys these advertisements, the demand for its Monday night buy-by-the-pound lobster special increases, but these ads are not free. The inverse demand function for Roger's Monday night special is: 

P = 90 + (2 x A) - (0.75 × Q), 

where P is the per-pound price charged, Q is the number of pounds of lobster that Roger's sells each Monday night, and A is the number of radio ads that Roger's purchases each week. Roger's marginal cost of selling lobster is:

MC(Q) = (0.5 x Q),

which implies that the total cost function is:

TC(Q) = (0.25 x Q2)

a.Suppose A=2. Identify the profit-maximizing quantity of lobster (in pounds) that Roger's sells each Monday.

b.Suppose A=2. What per-pound price does Roger's charge for lobster?

c.Suppose A=2. How much profit does Roger's Lobsters earn each Monday?

d.Suppose A=3. Identify the profit-maximizing quantity of lobster (in pounds) that Roger's sells each Monday.

e.Suppose A=3. What per-pound price does Roger's charge for lobster?

f.Suppose A=3. How much profit does Roger's Lobsters earn each Monday?

g.What is the marginal benefit of Roger's third radio advertisement?