Two different fabric materials can be produced at one facility, each takes one hour per ton to produce. Both exhibit diseconomies of scale: If x$1$ tons of the first are produced, the contribution is $6$x$1($x$12/2).$ For the second material, for x$2$ tons produced, the contribution is $(50$x$2).$ The facility can work $23$ hours per day $($one hour is required for maintenance$)$ and, because of raw materials availability, no more than $10$ tons of the first material and $18$ tons of the second can be produced daily. a$)$ Formulate the mathematical model.b$)$ Solve the model. What is the optimal daily production schedule to maximize contribution?