I have a linear program which I can't write its equations. The problem is An office furniture company has two plants that produce lumber used in the manufacturing of a line of desks and computer tables that the company sells. In one week, plant $A$ can produce the lumber required to manufacture 200 desks and 120 computer tables, while in one week, plant $B$ can produce the lumber to manufacture 350 desks and 240 computer tables.
Suppose it costs \$5,150 per week to operate plant $A$ and \$8,200 per week to operate plant $B$.
If the company needs enough lumber to manufacture at least 2,000 desks and 1,320 computer tables, how many weeks should each plant operate in order to meet this requirements at the a minimum cost? What is the minimum cost?
Thank you in advance.
How to set up the problem:
What is the objective? - Minimise the cost
Total cost = Cost of operating plant A + Cost of operating plant B
Now, we need to introduce variables to quantify this. Let $w_A$ be the number of weeks to run plant A, and similarly $w_B$
Now, total cost $C$ is given as
$$C = 5150w_A + 8200w_B$$
What are the constraints?
You need to produce a certain amount of lumber to satisfy the demand. How can we use our variables above to express that? We need a total of atleast $2000$ desks and $1320$ computer tables
Hence, the number of desks we would produce is $200w_A + 350w_B \geq 2000$
Similarly, for the tables we have $120w_A + 240w_B \geq 1320$
Put it all together, you get
$$\min 5150w_A + 8200w_B \\ \text{s.t} \\ 200w_A + 350w_B \geq 2000 \\ 120w_A + 240w_B \geq 1320 \\w_A, w_B \geq 0$$