A profit-maximizing firm produces one output, y, and uses one input, x, to produce it. The price per unit of the factor is denoted by w and the price of the output is denoted by p. You observe the firm's behavior over three periods and find the following: Period y x w p
1 1 1 1 1
2 2.5 3 0.5 1
3 4 8 .25
a. Write an equation that gives the firm's profits, pi, as a function of the amount of input x it uses, the amount of output y it produces, the per-unit cost of the input w, and the price of output p.
b. With output on the vertical axis and input on the horizontal axis, draw an isoprofit line for each of the three periods. What are the equations for these lines?

Galwaysc electronics makes two products. model a requires component a and component c. model b requires component b and component c. new versions of both models are released each year with updated versions of all components. all components are sourced overseas, and abc contracts annually for a quantity of each component before seeing that year’s demand. components are only assembled into finished products once demand for each model is known. for the coming year, alwaysc’s purchasing manner has proposed ordering 500,000 units of component a, 630,000 of component b, and 1,000,000 units of component c. her boss has asked why she has recommended purchasing so much of components a and b when alwaysc will not have enough of component c to fully use all of the inventory of a and b. what factors might the purchasing manager cite to explain her recommended order? explain your reasoning.