Currently, immunotherapy represents a cancer treatment and is commonly considered in combination with chemotherapy. This approach is particularly relevant for malignancies associated with impaired immune function. In this work, an ordinary differential equation (ODE) model is formulated as a mathematical framework for describing interactions between tumor and immune cells. Macrophage polarization together with cytokine dynamics is incorporated through pharmacokinetic-pharmacodynamic assumptions to provide a more detailed representation of tumor-immune interactions. The limited number of studies addressing these mechanisms within chemo-immunotherapy models motivated the development of this ODE framework. The positivity of solutions, equilibrium states, and their stability properties are analyzed. Furthermore, sensitivity of the final tumor population and the response time to initial conditions and parameter values is examined. The initial state of the adaptive immune system, as well as parameters governing tumor-cell proliferation, tumor carrying capacity, and the fractional exponent for CD8+ T-cell-mediated tumor-cell killing, strongly influences both the final tumor burden and the tumor-growth response time. Subsequently, numerical simulations are conducted for pulsed chemotherapy, pulsed immunotherapy, and combined chemo-immunotherapy, and the resulting responses are compared. Three patients exhibiting different immune responses are considered to demonstrate how immune activity can affect treatment strategies. Numerical results indicate that combining immunotherapy with chemotherapy can enhance tumor-control dynamics. Furthermore, the simulations reveal that immune-system strength plays a substantial role in determining cancer treatment outcomes.