State the linear programming problem in mathematical terms, identifying the objective function and the constraints.A firm makes products A and B. Product A takes 3 hours each on machine L and machine M; product B takes 3 hours on L and 2 hours on M. Machine L can be used for 13 hours and M for 8 hours. Profit on product A is $7 and $10 on B. Maximize profit.

Formulate but do not solve the following exercise as a linear programming problem.A division of the Winston Furniture Company manufactures x dining tables and y chairs. Each table requires 40 board feet of wood and 2 labor-hours. Each chair requires 16 board feet of wood and 4 labor-hours. In a certain week, the company has 2800 board feet of wood available and 560 labor-hours.If the profit for each table is $50 and the profit for each chair is $18, how many tables and chairs should Winston manufacture to maximize its profits P in dollars? Maximize      P  =             subject to the constraints board feet             labor-hours                     x ≥ 0         y ≥ 0

Formulate but do not solve the following exercise as a linear programming problem.A division of the Winston Furniture Company manufactures x dining tables and y chairs. Each table requires 40 board feet of wood and 2 labor-hours. Each chair requires 16 board feet of wood and 5 labor-hours. In a certain week, the company has 2800 board feet of wood available and 500 labor-hours.If the profit for each table is $50 and the profit for each chair is $18, how many tables and chairs should Winston manufacture to maximize its profits P in dollars? Maximize      P  =             subject to the constraints board feet             labor-hours                     x ≥ 0         y ≥ 0

which options are correct ?