[24 Points] Sackville Plastics is considering the acquisition of a new packaging machine that will apply a plastic film over a product and attach it to a cardboard backing. Hamamatsu Techwrap manufactures 3 models of packaging equipment that would meet Sackville's requirements. They are intended for low, medium, and high-volume applications. The costs of the three machines are $22,000, $31,000, and $47,000, respectively. Sackville estimates that the packaging cost per unit, including materials, labour and equipment maintenance will be $0.22, $0.19, and $0.15, respectively. a. [4 point] Construct the three cost functions, depending upon which machine is selected. b. [4 point] Under what conditions is the low volume machine preferable? c. [4 point] When is the high-volume machine preferred? d. [12 point] Graph the three cost functions and identify the volumes at which each machine is the least costly.