This paper presents a new linear programming approach for throughput maximization on the uplink of a multiclass variable spreading gain code-division multiple-access (CDMA) multicellular system in Rayleigh fading for both binary phase-shift keying (BPSK) and quaternary phase-shift keying (QPSK) modulations. Based on the improved Gaussian approximation technique, we derive exact closed-form expressions of the outage probability, which are used as a physical (PHY) layer constraint of the maximization problem. We show that it is possible to transform the nonlinear constraint into a set of equivalent linear expressions. This facilitates the formulation of a new linear throughput maximization that noticeably requires less computational complexity than the known nonlinear approaches. Furthermore, due to the simplicity of the linear approach, we can include the constraints of such higher layers, i.e., media access control (MAC) and call admission control (CAC) layers, into the proposed formula. Accordingly, we introduce two linear programming optimization formulas. One is for MAC-PHY optimization, and another is for cross-layer optimal CAC policy. In the case of MAC-PHY optimization, the throughput is maximized, at low background noise level, when every user retains the same bit energy, particularly in the case where the difference in data rates is high. Nonetheless, at high levels of background noise, the throughput would be maximized when a larger amount of bit energy is allocated to the high-rate users. For the joint optimal policy, the throughput and the blocking probability are optimized and improved up to 50% in comparison to those of the conventional CAC policy, which is known as the complete sharing policy.