A plant manufactures two types of items: S-item and T-item. A S-item sells for $27 and uses $10 worth of raw materials. Each S-item that is manufactured increases the company's variable costs by $14.
A T-item sells for $21 and uses $9 worth of raw materials. Each T-item built increases the company's costs by $10. The manufacture of the two items requires two types of skilled labor: carpentry and finishing. A S-item requires 2 hours of finishing labor and 1 hour of carpentry labor.
A t-item requires 1 hour of finishing and 1 hour of carpentry labor. Each week, the plant can obtain all the needed raw material but only 100 finishing hours and 80 carpentry hours. Demand for T-item is unlimited, but at most 40 S-items are bought each week.
The plant wants to maximize weekly profit (revenues _ costs).
Formulate a mathematical model that can be used to maximize profit.