maximizing profits in matrix

An aircraft manufacturer can produce three different types of aircraft: small, medium, and large. Aircraft costs consist of a materials cost and a labor cost. The small aircraft sells for $40 million more than its materials cost, the medium aircraft sells for $ 50 million more than its materials cost, and the large air- craft sells for $75 million more than its materials cost. Labor cost for each aircraft consists of three parts: fuselage production at $32/hour, wing produc- tion at $45/hour, and assembly at $30/hour. Constructing 1 small aircraft requires .1 million man hours (mmh) of fuselage production, .22 mmh of wing production, and .15 mmh of assembly. Constructing 1 medium aircraft requires .23 mmh of fuselage production, .25 mmh of wing production, and .17 mmh of assembly. Constructing one large aircraft requires .31 mmh of fuselage production, .38 mmh of wing production, and .27 mmh of assembly. The following constraints are placed on production:

1. Fuselage production facility can accommodate a maximum of 5 mmh.

2. Wing production facility can accommodate a maximum of 7 mmh.

3. In order to receive a needed tax break, the fuselage production facility must have at least 4 mmh.

4. As they have an overlapping workforce, the combined wing production and assembly labor must not exceed 15 mmh.

5. Due to limited large scale faciliities, labor spent on assembly of the large aircraft must not exceed 2 mmh.

6. To fulfill existing contracts, the number of small aircraft produced must be greater than 2.

7. To fulfill existing contracts, the number of medium aircraft produced must be greater than 3.

8. To fulfill existing contracts, the number of large aircraft produced must be greater than 1.

You will be trying to find numbers of small, medium, and large (S, M, and L) aircraft whose production maximizes profit.

how would i make a column matrix f, such that f’*[S;M;L] is the net profit in millions of dollars (note: this profit should be in millions of dollars, so if the net profit were $4 million, f’*[S;M;L]=4).