Pls help with this problem!

Suppose that Michelin is the only producer of tires and Toyota the only producer of cars. The demand function for cars is given by Q = 40 - 4P. Michelin's (constant) cost of production for a set of five tires is $3. The production of one car requires a set of five tires plus a bundle of inputs. Toyota can obtain this bundle of inputs at a (constant) cost of $6. Suppose first that Michelin and Toyota are just two departments within the same vertically integrated monopoly (Firm V). (a) What would be the marginal cost of car production for this vertically integrated Firm V? (b) What price would Firm V firm charge for cars and how many cars would it produce? (c) Calculate Firm V's profit and consumer surplus under this market structure. Suppose now that Michelin and Toyota are separate firms, each a monopoly in its own industry. Michelin quotes a price $w for a set of five tires and Toyota decides how many sets to buy at that price. Now, Toyota's costs per car includes buying a set of tires from Michelin at $w plus the bundle of other inputs at $6. We will view this as a two-stage game, where Michelin decides on $w in Stage 1 and in Stage 2 Toyota decides how many cars to sell (and, hence, how many sets of tires to buy from Michelin) as a function of Sw. Remember that this type of an extensive form game is solved using backwards induction. However, since the strategies are not a discrete set of choices, we will not use a game tree. Instead let us solve for the equilibrium using the steps listed in the sub-parts below. Broadly, Toyota chooses profit-maximizing quantity of cars to sell as a function of w and Michelin sets w to maximize its own profits, given Toyota's demand for tires. (d) Calculate profit-maximizing quantity of cars (Or) that Toyota will sell as a function of w? (e) Now, calculate the price (py) that Toyota will charge the consumers as a function of w. (f) Given Toyota's choice of Oy, Michelin now faces a demand for Or number of tires. Solve for Michelin's profit-maximizing choice of w. [Hint: This optimization, unlike the usual profit-maximization, is carried out with MR and MC for Michelin as a function of w.] (g) Substituting the answer calculated for w, now find the quantity of cars Or sold by Toyota and the price py charged by Toyota to the consumers