XYZ Inc Produces Two Types of Exercise Machines-Multi-Purpose, Which Can Be

Essay

XYZ Inc. produces two types of exercise machines-Multi-purpose, which can be used for cardiac fitness, fat loss, weight reduction etc., and Cardiac, just for cardiac fitness. Each unit of Multi-purpose generates a contribution of $\$ 300.00$ , while each unit of Cardiac produces a contribution of $\$ 200.00$ . Each Multi-purpose requires 7 man-hours of assembly time and 2 man-hours of packing and shipping time. It also uses 5 pounds of specialized steel in limited supply. Each unit of Cardiac requires 5 man-hours of assembly time and 1 man-hour of packing and shipping time. It also uses 7 pounds of specialized steel in limited supply. Assembly man-hours available per month are 500; packing and shipping manhours available per month are 150 . The number of units of specialized steel available per month is 600 pounds. The sales department has imposed a restriction limiting the number of Multi-purpose machines produced to not exceed double the number of Cardiac machines produced per month. Formulate a linear programming model that would maximize profit subject to the constraints. Solve the problem using the graphical method.