Given the following utility function: U = 10X + 2Y and marginal utilities: MU_x = 10, MU_y = 2 A consumer facing the following prices: P_x = $1, P_y =2 chooses to consume: 11 units of good X and 16 units of good Y. Assume that graphically good X is on the horizontal axis and good Y is on the vertical axis. Given this consumption bundle, the marginal rate of substitution is equal to - (Note that the minus sign is already included.).

Burke enterprises is considering a machine costing $30 billion that will result in initial after-tax cash savings of $3.7 billion at the end of the first year, and these savings will grow at a rate of 2 percent per year for 11 years. after 11 years, the company can sell the parts for $5 billion. burke has a target debt/equity ratio of 1.2, a beta of 1.79. you estimate that the return on the market is 7.5% and t-bills are currently yielding 2.5%. burke has two issuances of bonds outstanding. the first has 200,000 bonds trading at 98% of par, with coupons of 5%, face of $1000, and maturity of 5 years. the second has 500,000 bonds trading at par, with coupons of 7.5%, face of $1000, and maturity of 12 years. kate, the ceo, usually applies an adjustment factor to the discount rate of +2 for such highly innovative projects. should the company take on the project?