Problem 2 (1 point). Using the Left Reinmann sum with n=4, estimate f 2 1 dx. 0 x+0.5 Problem 3 (10 points). 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 rm employes 500 people and produces 1200 units of product. a) b) d) (3 points) Using integrals, nd the production anction Q(x), i.e., nd how much the rm will produce (Q) as a function of how many people it employs (x). (3 points) If the wage is equal to $100 per worker and the rm is able to sell its product for $70 per unit, how many people the rm needs to employ to maximize its prot? Note that the prot is equal to H = 70Q 10026. Note also that you will have to use the knowledge from previous chapters. (1 point) Without performing any calculations, state how your answer to part (b) will change (increase, decrease, or stay the same) if the rm with 500 employees would have produced 1300 units of product instead of 1200. Assume all other information remains the same. (3 points) A competitor rm has access to a better technology and has a larger marginal product of labor of (3:320 + 60001"). By how much the total output of this rm will increase if it increases its current staff from 700 to 1000 employees? Round your answer to the nearest integer number