Home Goods Inc. $($HG$)$ makes custom sofas to order, receiving detailed customer order information via a network of$$retailers$.$ Once a customer picks the style of his$/$her sofa with additional specifications such as its size, fabric and$$finishing$,$ the retailer emails the orders to HG Inc. The most basic sofa is the SuperSoft Sofa which HG Inc. manufactures$$according to the following process.$$First$,$ Greg checks the order for consistency and prepares instructions for the subsequent operations. When the process$$operates at capacity, Greg$$s utilization is $50\%.$ Once Greg is done, the order moves to both Eddy and Lance who can work$$on their respective tasks in parallel. Eddy builds the correct sized frame and spray paints the frame using HG$$s instant Dry$$technology$.$ After the painting operation, he fills the frame with synthetic stuffing and covers it with light canvas. This$$takes Eddy $20$ min. When the process operates at capacity, Eddy$$s utilization is $100\%.$ When the frame is ready, Eddy$$passes it onto final assembly and finishing $($FAT$).$ Lance is in charge of fabric preparation. Lance selects and cuts the$$fabric to the right sofa size. When the process operates at capacity, he is busy $40\%$ of the time. Once the fabric is ready,$$Lance passes them onto Miguel, who makes cushions from half of the cut fabric. Miguel requires $10$ minutes for his task$$and his utilization is $50\%.$ When done, Miguel passes the prepared cushions and the remaining fabric to final assembly$$and finishing. At final assembly and finishing, there is one worker named Tyler, who performs this step. Tyler picks the$$frame of the sofa, covers it with the remaining fabric and installs its cushions. Finally, the finishing touches are given$$before the sofa is sent to logistics department for delivery. When operating at capacity, Tyler$$s utilization is $60\%.[$Utilization $=$ Process Capacity$/$Resource Capacity$]$