A textile company produces tablecloths and cloth napkins. The production process includes two steps: cutting and sewing. Every day at least 2 production hours must be worked in the cutting department and 6 production hours must be worked in the sewing department. The time needed for cutting and sewing each item as well as the production costs for each item are provided in the table below: Product Time Needed to Cut FabricTime Needed to SewProduction Costs Tablecloths 8 minutes 9 minutes $9.50 Cloth Napkins1.5 minutes 6 minutes $3.50
Let X represent the number of tablecloths to be produced and let X represent the number of cloth napkins to be produced. What is the equation of the objective function Z that optimizes the production cost?