A company manufacturers two types of paint called A and B. With each barrel of A that they produce they earn a profit of $11 and with each barrel of B that they produce they earn a profit of $20. Each type of paint must first go through a blending station and then a mixing station and finally an inspection station. For each barrel of Product A produced twenty-two minutes are required in the blending station, twelve minutes are required in the mixing station and ten minutes are required in the inspection station. For each barrel of Product B produced fourteen minutes are required in the blending station, sixteen minutes are required in the mixing station and twenty-five minutes are required in the inspection station. On any given twenty-four hour day in which the operation runs, there are 3080 man-minutes available in blending, 1920 man-minutes available in mixing and 2500 man-minutes available in inspection.
A couple of other factors that might need to be taken into consideration are these:
• In any given twenty-four hour day, only 217 barrels are available so the total number of barrels produced cannot exceed this amount;
• Because of union rules at least 25 barrels of each type must be produced each day;
• If the optimal quantities are not whole numbers of barrels, it's okay and it should be round to two decimal place accuracy;
• The optimal profit should be rounded to the nearest penny.

A) How many barrels of each type of paint should they produce in order to maximize their profit