Suppose that an athletic gear company produces running shoes according to the following production function, f(x1,x2)=x11/2x21/4, where x1 denotes labour and x2 denotes capital. The price of a pair of running shoes is 4 . The price of factor 1 , labour, is denoted w1, while the price of capital is denoted w2 a) Using the production function, write an equation that says that the value of the marginal product of factor 1 is equal to the price of factor 1 , and an equation that says that the value of the marginal product of factor 2 is equal to the price of factor 2. Solve two equations in the two unknowns, x1 and x2, to give the amounts of factors 1 and 2 that maximize the company's profits as a function of w1 and w2. b) If the price of factor 1 is equal to 2 , and the price of factor 2 is equal to 1 , how many units of factor 1 will the company demand? How many units of factor 2 will it demand? How much output will it produce? Finally, how much profit will it make? Suppose that an athletic gear company produces running shoes according to the following production function, f(x1,x2)=x11/2x21/4, where x1 denotes labour and x2 denotes capital. The price of a pair of running shoes is 4 . The price of factor 1 , labour, is denoted w1, while the price of capital is denoted w2 a) Using the production function, write an equation that says that the value of the marginal product of factor 1 is equal to the price of factor 1 , and an equation that says that the value of the marginal product of factor 2 is equal to the price of factor 2. Solve two equations in the two unknowns, x1 and x2, to give the amounts of factors 1 and 2 that maximize the company's profits as a function of w1 and w2. b) If the price of factor 1 is equal to 2 , and the price of factor 2 is equal to 1 , how many units of factor 1 will the company demand? How many units of factor 2 will it demand? How much output will it produce? Finally, how much profit will it make