mthematics

Question No. 1(12 points) (a) Find - for each of the following functions: 2x + 5x - 2 3x3 + 5x+3. (i)y = ((2x] + 6) (7x - 5)) . (iID) y - (5x - 10)e-2x4+8 (b) A one - product firm estimates that its daily total cost function is ((x) - x - 6x3 + 15x + 15 and its total revenue is R(x) - 30x. Find the value of x that maximizes the daily profit Question No. 2(12 points) (a) Find the point elasticity of the demand equations for the indicated values of p, and determine whether demand is elastic, inelastic or has unit elasticity: p = 10-0.04q, q = 100 (b) A manufacturer'smarginal - cost functonis = = 0.6q + 2. If production is presently set at q - 80 units per week, how much more would it cost to increase production to 100 units per week? Question No. 3(10 points) (a) Evaluate each of the follwoing integrals: (of (e* + 3x' + 2xjax, (1) dx, (uil) 4x* (30 + x3)3 dx (b) Find the total cost if the marginal cost is given by = 0.08q' - 106q +6.5. {fixed cost = 8000} and q - 25. Question No. 4 (6 points) For a particular urban group, sociologists studied curernt average yearly income y (in dollars)taht a person can expect to reicieve with x years of eduaction before seeking regular employment. They estimated that the rate at which income changes with respect to education is given by -100xi, Where y = 28,720 when x = 9. Find y