The Simple Machine Company makes Widgets, Gadgets, and Gizmos out of pulleys, wedges, and levers. Each Widget requires 2 pulleys, 1 wedges, and 3 levers. Each Gadget requires 2 pulleys, 3 wedges, and...

Extracted text: The Simple Machine Company makes Widgets, Gadgets, and Gizmos out of pulleys, wedges, and levers. Each Widget requires 2 pulleys, 1 wedges, and 3 levers. Each Gadget requires 2 pulleys, 3 wedges, and 1 lever. Each Gizmo requires 1 pulley and 2 levers. If the company has 20 pulleys, 6 wedges, and 34 levers available, how many Widgets, Gadgets, and Gizmos can be made to use up all of the resources? Name the variables, set-up a system of equations, solve it, and give all possible realistic answers.