8. Reconsider the newspaper problem of Exercise 7, but now suppose that advertisers have the option of using direct mail to reach their customers. Because of this, management has decided not to increase the price of advertising beyond S400/page. (a) Find the weekly subscription price and the advertising price that will maximize profit. Use the five-step method, and model as a con- strained optimization problem. Solve by the method of Lagrange multipliers. (b) Determine the sensitivity of your decision variables (subscription price and advertising price) to the assumption of 5,000 lost sales when the price of the paper increases by ten cents (c) Determine the sensitivity of the two decision variables to the assump- tion of 50 pages of advertisements lost per week when the advertising price increases by $100/page. (d) What is the value of the Lagrange multiplier found in part (a)? Inter- pret this number in terms of the sensitivity of profit to the 8400/page assumption. 8. Reconsider the newspaper problem of Exercise 7, but now suppose that advertisers have the option of using direct mail to reach their customers. Because of this, management has decided not to increase the price of advertising beyond S400/page. (a) Find the weekly subscription price and the advertising price that will maximize profit. Use the five-step method, and model as a con- strained optimization problem. Solve by the method of Lagrange multipliers. (b) Determine the sensitivity of your decision variables (subscription price and advertising price) to the assumption of 5,000 lost sales when the price of the paper increases by ten cents (c) Determine the sensitivity of the two decision variables to the assump- tion of 50 pages of advertisements lost per week when the advertising price increases by $100/page. (d) What is the value of the Lagrange multiplier found in part (a)? Inter- pret this number in terms of the sensitivity of profit to the 8400/page assumption