An electronics company is planning its production next quarter for its two product lines, relays and capacitors. The profit contribution is $250 for a case of relays and $200 for a case of capacitors. Three resources limit how much of each product the company can produce: labor, stamping capacity, and testing capacity. Next quarter 80,000 labor hours will be available; a case of relays requires 200 labor hours and a case of capacitors requires 150 labor hours. The stamping machine will be available for 1,200 hours next quarter, and a case of relays requires 4 hours on the stamping machine and a case of capacitors requires 2 hours on the stamping machine. Relays require 3 hours of testing per case and capacitors require 5 hours of testing per case. The testing machine will be available for 2,000 hours next quarter. How many cases of relays and capacitors should the company produce next quarter to maximize profit?

Let X₁ = cases of relays produced next quarter

X₂ = cases of capacitors produced next quarter