Problem 2 Pat is the type to plan everything in advance, and she is already starting to plan for retirement. She plans to work for 40 years, and then retire for the following 30 years. She expects to spend $100,000 in her first year of retirement, with a 2% growth rate. She will increase her working-years savings rate by 5% per year. While working, she expects her account will have a 6.75% return, and during retirement it will have a 4.75% return. After the 30th year of retirement, she wants to have $200,000 in her account for safety net and bequest reasons (It is fine if the amount is not exactly $200,000 due to rounding error). Her retirement savings account currently has $0. To solve the problem, determine how much Pat needs to save in year 1 to accomplish her retirement goals (use Solver or Goal Seek).

Problem 3 Lets build on the pizza parlor example from the notes. In addition to selling cheese pizzas for $7, supreme pizzas for $12 and calzones for $6, the pizza parlor will also sell vegetarian pizzas for $10.50 and pepperoni pizzas for $9.75. Because of limitations to the quantity of ingredients and oven capacity, the pizza parlor has the following constraints: Can only make 950 total items a day Can make a maximum of 550 pizzas total Can make a maximum of 250 supreme pizzas Can make a maximum of 300 pizzas containing peppers (this includes the supreme and vegetarian pizza) Taking these constraints into account, what quantity of each item does the pizza parlor need to sell to maximize revenue? You need to use Solver.

Can you include formulas for how to solve these?