Q1. Using the Lagrangian method, solve the following problem. I. e., write down the Lagrangian, the FOCs, and find (x ∗ , y∗ ) and λ ∗ . Find f(x ∗ , y∗ ). Max f(x, y) = x 1 2 y 1 2 subject to x + 2 5 y = 4.

Magic realm, inc., has developed a new fantasy board game. the company sold 15,000 games last year at a selling price of $20 per game. fixed expenses associated with the game total $182,000 per year, and variable expenses are $6 per game. production of the game is entrusted to a printing contractor. variable expenses consist mostly of payments to this contractor. required: 1-a. prepare a contribution format income statement for the game last year.1-b. compute the degree of operating leverage.2. management is confident that the company can sell 58,880 games next year (an increase of 12,880 games, or 28%, over last year). given this assumption: a. what is the expected percentage increase in net operating income for next year? b. what is the expected amount of net operating income for next year? (do not prepare an income statement; use the degree of operating leverage to compute your answer.)

Which of the following statements is true of unsought products? as compared to convenience products, unsought products are purchased more frequently. unsought products are consumer products and services that customers usually buy frequently, immediately, and with minimal comparison and buying effort. a life insurance policy is an example of an unsought product. unsought products have strong brand identification for which a significant group of buyers is willing to make a special purchase effort. unsought products are those products purchased for further processing or for use in conducting a business.

Lead time for one of your fastest-moving products is 20 days. demand during this period averages 90 units per day. a) what would be an appropriate reorder point? ) how does your answer change if demand during lead time doubles? ) how does your answer change if demand during lead time drops in half?