Help please

Question 1 The owner of a textile factory that makes hockey sweaters finds that it costs $2,500 to produce 100 sweaters in one day and $5,950 to produce 250 sweaters in one day. a) Assuming that the cost function is linear, show that it is C(x) = 23x + 200 where x is the number of sweaters produced in one day. b) Suppose that the factory must sell all the sweaters that they produce in a day. This means that the price of the sweaters may change depending on how many need to be sold. This scenario is modelled by the revenue function R(x) = -x2 +53x. What is the minimum number of sweaters that needs to be sold in a day in order to cover the cost of producing the sweaters? c) Graph the profit function P(x) = R(x) - C(x) , where x is the number of sweaters sold in a day. d) Use the graph of the profit function to determine how many sweaters should be produced in order to maximize profits