Afood mix is to be made that would balance the amount of methionine (met), a limiting amino acid in terms of food protein nutritional value, by blending several types of plant proteins. corn, which contains 16% protein, has 1.3 g met/100 g protein; soy flour with 50% protein has 1.8 g met/100 g protein; and nonfat dry milk with 40% protein has 3.1 g met/100 g protein. how much of these ingredients must be used to produce 100 kg of formula that contains 25% protein and 2.3 g met/100 g protein.

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.]