Suppose we have the following data from a single question about vehicle choice with the following attributes: p = price (in thousands), x1 = fuel economy (in mpg), and x2 = 0-60 acceleration time (in seconds), where nj is the number of people who chose alternative j and 0 is the no-choice option (the outside good).ABCDOp ($1000s)15152025-x1 (mpg)25352535-x2 (sec)6886-nj50201524Assume a logit model with utility linear in the parameters, so that vj=\beta0*pj+\beta1*x1j+\beta2*x2j+ \beta3*yjOGv \forallj\in \left \{ A, B,C, D,O \right \}, yjOG=1 for the outside good and 0 otherwise, and \beta _{3} is the utility of the outside good. a)Write the maximum (log) likelihood formulation as a standard optimization problem. b)Use Excel Solver to determine the betas that maximize likelihood. Report the resulting betas with their standard errors. c)Does the solution satisfy first and second order optimality conditions? Justify your answer. d)Do the signs of the beta values match what you would expect? Explain why or why not. e)For each of the attributes (price, mpg, and acceleration), does the entire 95% credible interval for beta have the same sign? What could you do to further reduce uncertainty in the betas?f)What is the expected average willingness to pay for a 1 mpg increase, ceteris paribus (you do not need to compute confidence intervals)?g)Suppose a new product N were added to this market with price $15,000, efficiency 30mpg, and acceleration 7 seconds. Simulate expected share for N given a choice among the alternatives {A, B,C, D,N, O}? What is the expected value and the 95% credible interval of the expected share for N?h)What is the maximum price that could be charged for N while still capturing at least 10% expected share?i)What is the maximum price for N at which the 95% credible interval of expected share lies above 10%?j)What value of price maximizes expected revenue?