Project Business and Economics Aplications: Marginal Analysispaul vazMaximizing ProfitAn appliance firm is marketing a new refrigerator. It determines that in order to sell x refrigerators the price in dollars per refrigerator must be .4.0280 xp It also determines that the total cost in dollars of producing x refrigerators is given by the function.6.05000)(2xxC (a) Assuming that the number refrigerators sold is equal to the number of refrigerators produced, find the total revenue function)(xR(b) Graph the cost and the revenue (in the same frame) and find break-even points from the graphs. (c) Estimates from graphs: From the graphs, estimate the number of refrigerators the company must produce and sell in order to maximize profit. Estimate this maximum profit from the graphs. (i) number of refrigerators:____________________________(ii) maximum profit: _________________________________)(xR(d) Verification of the estimates obtained in (c) using Maximum - Minimum Principles: (i) Find the total profit function)(xP:_________________________________ (ii) Find the critical point of )(xP:____________________________ (iii) Use the 2nd Derivative Test to determine whether you have a maximum or a minimum at the critical point. (iv) Find the maximum( or minimum) value of the Profit at the critical point. [ Compare your answer here to your answer in (c) (ii)](e) Marginal Analysis(i) Find the marginal cost )(' xC. (ii) Find the marginal revenue )(' xR. (iii) Find the value of x for which the marginal cost is equal to the marginal revenue. [Compare your answer here to your answers in (c) (i) and (d) (ii) ] (iv) Use the value of x obtained in (e) (iii) in the Profit-function to find the corresponding profit. [Compare your answer here to your answers in (c) (ii) and (d) (iv)
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