Cement company makes bags of cement by two substances. Kilogram of the substance A costs $2,4$ CZK and consist of $4$ units of high quality sand, $3$ units of raw sand and $5$ units of gravel. Kilogram of the substance B costs $4\mathrm{????}\mathrm{????}\mathrm{????}$ consists of $\mathrm{????}3$ units of high quality sand, $6$ units of raw sand and $2$ units of gravel. Each bag has to contain at least $120$ units of high quality sand, $120$ units of raw sand and $100$ units of gravel. Company is searching for best combination of both substances to minimize expenses.

Design mathematical model of the problem.

Find the optimal solution by simplex method.