11.16 Burrs are considered a major problem in machining operations, punching, or casting processes. Many applications require that all burrs and sharp edges be removed to the extent that material fragments are not visible and sharpness cannot be felt. A manufacturer produces a cost-effective deburring tool that removes burrs and sharpness. The manufacturer intends to sell the tool (excluding warranty cost) for $22 and provides a lump sum warranty for a six-month duration. The annual production is 6000 tools, and the manufacturer intends to invest the warranty fund at an interest rate of 4% per year and increase the price by 3% after six months. Assume that the tools experience a constant failure rate of 0.006 failures/month. Determine the price of the tool including warranty cost, the proportion of the lump sum rebate to be paid to the customer when the tool fails before six months, and the total warranty reserve fund.