You would like to make a nutritious meal of eggs, mixed vegetables and brown rice. the meal should provide at least 35 g of carbohydrates, at least 30 g of protein, and no more than 45 g of fat. one serving of eggs contains 2 g of carbohydrates, 18 g of protein, and 12 g of fat. a serving of mixed vegetables contains 14 g of carbohydrates, 15 g of protein, and 8 g of fat. a serving of rice contains 40 g of carbohydrates, 6 g of protein, and 1 g of fat. a serving of eggs costs $4, a serving of mixed vegetables costs $3.50, and a serving of rice costs $3. (a) formulate a linear optimization model that could be used to determine the number of servings of eggs, mixed vegetables, and rice for your meal that meets the nutrition requirements at minimal cost. (b) use excel solver to find the optimal solution. submit your excel file. (c) report the optimal solution.

Suppose a firm faces a fixed price of output, 푝푝= 1200. the firm hires workers from a union at a daily wage, 푤푤, to produce output according to the production function 푞푞= 2퐸퐸12. there are 225 workers in the union. any union worker who does not work for this firm is guaranteed to find nonunion employment at a wage of $96 per day. a.what is the firm’s labor demand function? b.if the firm is allowed to choose 푤푤, but then the union decides how many workers to provide (up to 225) at that wage, what wage will the firm set? how many workers will the union provide? what is the firm’s output and profit? what is the total income of the 225 union workers? c.now suppose that the union sets the wage, but the firm decides how many workers to hire at that wage (up to 225). what wage will the union set to maximize the total income of all 225 workers? how many workers will the firm hire? what is the firm’s output and profit? what is the total income of the 225 union workers? [hint: to maximize total income of union, take the first order condition with respect to w and set equal to 0.]