Supply Chain - (with Excel)

Problem statement: A company produces three products: A, B, and C. The selling prices are $10, $20, and $30 respectively. Variable production costs are $3, $12, and $25 respectively. Demand for A is between 30 and 100 units, Demand for B is between 20 and 70 units, and demand for C is between 15 and 50 units.

All the products need to be produced at three machines M1, M2, and M3 with total capacity 300, 250, and 203 capacity units respectively.

Production of the product A seizes 2 capacity units at M1, 1 capacity unit at M2, and 2 capacity units at M3. Production of the product B seizes 3 capacity units at M1, 4 capacity units at M2, and 2 capacity units at M3. Production of the product C seizes 4 capacity units at M1, 5 capacity units at M2, and 2 capacity units at M3. Currently, the company produces 50 units of A, 25 units of B, and 12 units of C.

Questions: Is the decision to produce 50 units of A, 25 units of B, and 12 units of C optimal in regard to profit maximization? If yes, why? If not, what is optimal decision?