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Aviation electronics produces three types of switching devices. Each type involves a two step assembly operation. The assembly times are shown in the following table

Assembly time per unit $($minutes$)$

Station $1$ Station $2$

Model a $2\mathrm{.}53$

Model b $1\mathrm{.}81\mathrm{.}6$

Model c $22\mathrm{.}2$

Each workstation has a daily working time of $7\mathrm{.}5$ hours. Manager wants to obtain the greatest possible profit during the next $5$ working days. Model a yields a profit of Rs$.8\mathrm{.}25$ per unit, Model b yields a profit of Rs$.7\mathrm{.}50$ per unit, Model c yields a profit of Rs$.7\mathrm{.}80$ per unit. Assume that the firm can sell all its produces during this time but it must fill outstanding orders for $20$ units of each model type. Formulate the linear programming model of this problem.