Question: Manufacturing sierra Wood Products manufactures two high-quality products, rockers and bookshelf units. Its profit is $30 per rocker and $42 per bookshelf unit. Next week's production will be constrained by two limited resources, labor and wood. The labor available next week is expected to be at most 930 hours, and the amount of wood available is expected to be at most 2400 board feet. Each rocker requires 4 labor hours and 8 board feet of wood. Each bookshelf unit requires 3 labor hours and 12 board feet of wood. Find how many rockers and bookshelf units should be produced next week to maximize Sierra's profit. Find the maximum profit.
Problem: Manufacturing Sierra Wood Products manufactures two high-quality products, rockers and bookshelf units. Its profit is $30 per rocker and $42 per bookshelf unit. Next week's production will be constrained by two limited resources, labor and wood. The labor available next week is expected to be at most 930 hours, and the amount of wood available is expected to be at most 2400 board feet. Each rocker requires 4 labor hours and 8 board feet of wood. Each bookshelf unit requires 3 labor hours and 12 board feet of wood.
(a) Write the inequalities that describe the constraints on the number of each product produced next week. Begin by identifying what x and y represent.
(b) Graph the region determined by these constraint inequalities.