Atwater Chemicals produces an engine additive for machinery. The additive is produced by adding various ingredients to a petroleum$-$based lubricant. Atwater purchases the lubricant from two suppliers, Woodlawn Petroleum and Spokane Chemicals. The quality of the final product depends directly on the quality of the lubricant. If the lubricant is "off," Atwater has to dispose of the entire batch. Because all lubricant can be "off," Atwater uses a measure it calls the $$yield$,$ which is computed as

Yield $=$ Good output $-$: Input

where the output and input are both measured in barrels. As a benchmark, Atwater expects to get $12$ barrels of good output for every $16$ barrels of lubricant purchased for a yield of $75$ percent $(=12$ barrels of output $-$: $16$ barrels of lubricant$).$

Data on the two suppliers for the past year follow:

Woodlawn Petroleum Spokane Chemicals Total

Total inputs purchased $($barrels$)5,6003,4009,000$

Good output $($barrels$)3,6402,9246,564$

Average price $($per barrel$)$ $ $117\mathrm{.}00$ $ $150\mathrm{.}50$ $ $129\mathrm{.}66$

The sales manager of Woodlawn Petroleum has proposed to the purchasing manager at Atwater that Woodlawn be given an exclusive contract to supply the lubricant. If it receives the contract, Woodlawn will guarantee a $75$ percent yield on the lubricant it supplies.

Required:

a$.$ Assume that the average quality, measured by the yield, and prices from the two companies will continue as in the past. What is the maximum price for lubricant that Atwater Chemicals should be willing to pay Woodlawn Petroleum under the exclusive contract?

Note: Round your answer to $2$ decimal places.