In this paper, we consider the max-min signal-to-interference plus noise ratio (SINR) problem for the uplink transmission of a cell-free Massive multiple-input multiple-output (MIMO) system. Assuming that the central processing unit (CPU) and the users exploit only the knowledge of the channel statistics, we first derive a closed-form expression for uplink rate. In particular, we enhance (or maximize) user fairness by solving the max-min optimization problem for user rate, by power allocation and choice of receiver coefficients, where the minimum uplink rate of the users is maximized with available transmit power at the particular user. Based on the derived closed-form expression for the uplink rate, we formulate the original user max-min problem to design the optimal receiver coefficients and user power allocations. However, this max-min SINR problem is not jointly convex in terms of design variables and therefore we decompose this original problem into two sub-problems, namely, receiver coefficient design and user power allocation. By iteratively solving these sub-problems, we develop an iterative algorithm to obtain the optimal receiver coefficient and user power allocations. In particular, the receiver coefficients design for a fixed user power allocation is formulated as generalized eigenvalue problem whereas a geometric programming (GP) approach is utilized to solve the power allocation problem for a given set of receiver coefficients. Numerical results confirm a three-fold increase in system rate over existing schemes in the literature.