Backyard Equipment manufactures garden tillers, leaf blowers, and lawn mowers for home use in a mixed$-$model assembly line. Annual demand is estimated as $4500$ for garden tillers, $3000$ for leaf blowers, and $9000$ for lawn mowers. The plant is currently operating one shift at an overtime schedule of $25$ days per month. Backyard is pursuing the lean principles of uniform production and mixed$-$model assembly.

a$.$ Determine a mixed$-$model production sequence that satisfies the goals of smoothing component production and assembling a variety of products each sequence.

b$.$ How many times would the designed sequence be repeated per day to meet demand?