Hawkins Manufacturing Company produces connecting rods for $4-$ and $6-$cylinder automobile engines using the same production line. The cost required to set up the production line to produce the $4-$cylinder connecting rods is $$1800,$ and the cost required to set up the production line for the $6-$cylinder connecting rods is $$3000.$ Manufacturing costs are $$15$ for each $4-$cylinder connecting rod and $$20$ for each $6-$cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If there is a production changeover from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up$,$ the weekly production capacities are $61006-$cylinder connecting rods and $84004-$cylinder connecting rods.