with a preferably written solution, please help in finding answer to part d. thank you! Problem 3. The marginal product of labor (i.e., the increase in total output if onemore worker is employed) is equal to 5,000/x+2000 where x is the number or employees. Currentlythe firm employes 500 people and produces 1200 units of product.a) Using integrals, find the production function Q(x), i.e., find how much the firm willproduce (Q) as a function of how many people it employs (x).b) If the wage is equal to $100 per worker and the firm is able to sell its product for $70 perunit, how many people the firm needs to employ to maximize its profit? Note that theprofit is equal to π =70Q-100x. Note also that you will have to use the knowledge fromprevious chapters.c) Without performing any calculations, state how your answer to part (b) will change(increase, decrease, or stay the same) if the firm with 500 employees would haveproduced 1300 units of product instead of 1200. Assume all other information remainsthe same.d) A competitor firm has access to a better technology and has a larger marginal.(5,000/x+2000 + e-0.001x). By how much the total output of this firm will product of laborof increase if it increases its current staff from 700 to 1000 employees. Round youranswer to the nearest integer number.

Marginal Product of Competitor : MP = 5000/(x+ 2000 ) + e-0.001xInitial Staff = 700 Final Staff…

Problem 3. The marginal product of labor (i.e., the increase in total output if one more worker is employed) is equal to 5,000/x+2000 where x is the number or employees. Currently the firm employes 500 people and produces 1200 units of product. a) Using integrals, find the production function Q(x), i.e., find how much the firm will produce (Q) as a function of how many people it employs (x). b) If the wage is equal to $100 per worker and the firm is able to sell its product for $70 per unit, how many people the firm needs to employ to maximize its profit? Note that the