Chemlabs uses raw materials i and ii to produce two domestic cleaning solutions, a and b. the daily availabilities of raw materials i and ii are 150 and 145 units, respectively. one unit of solution a consumes 0.5 units of raw material i and 0.6 units of raw material ii. one unit of solution b uses 0.5 units of raw material i and 0.4 units of raw material ii. the profits per unit of solutions a and b are $8 and $10, respectively. the daily demand for solution a lies between 30 and 150 units, and that for solution b between 40 and 200 units. find the optimal production amounts of a and b (maximize total profit)