A hospital has a static number of ward beds, intensive care unit (ICU) beds, operating theatre (OT) hours, nurses and doctors and a weekly problem of allocating these resources between various departments and patients groups. This pressure is particularly strong in India, where there are roughly 1.6 hospital beds and 0.7 doctors available per 1,000 people, which is significantly lower compared to most of the larger economies in the world. This report focuses on the use of Operations Research (OR) in making these decisions and specifically on linear programming (LP). In depth analysis of two journal articles. The first, published in the European Journal of Operational Research by Blake and Carter (2002), is a linear goal programming model for determining the case mix of a Toronto teaching hospital following an 18% reduction in funding. In Naval Research Logistics, Mehrotra et al. (2020) develop a stochastic mixed-integer linear program to help allocate and share the stockpile of ventilators in the United States during COVID-19 between the states. For each paper we describe the real-life problem, the model, the solution method and its strengths and weaknesses. We then formulate a general LP for the problem of resource allocation at a hospital and solve a numerical example of our own, using Python. The illustration defines the binding resources and prices them with shadow prices, examines the sensitivity of the ICU capacity, and demonstrates how a 10% reduction in the nursing hours makes it necessary to make a decision between financial balance and service volume through goal programming.