Question $2.$ A manufacturing company produces expensive toys. Each toy sells for $$200$ and costs $$75.$ The company incurs a fixed cost of $$6,000$ per day to lease their machines to manufacture the toys. Depending on the volume of production the company must also hire and schedule enough number of employees to carry out the production. The additional labor costs are $$500,$ $$1000$ and $$2500$ per day, when the production volume is $0$ to $30$ units, $31$ to $60$ units, and $61$ to $90$ units per day, respectively. The company forecasts the daily expected demand for its toys to be $75$ units.