Woodworks Industries Inc. produces a variety of products. In a particular manufacturing process, two types of wood, mahogany and pine along with the carpenters are the main resources of the company. The company is planning to introduce a new type of closet, a new set tables and office chairs using these three main resources.The requirements of each product for each resources is given in the table below. Constraints:1. Number of chairs should be more than 4 times the number of tables.2. Number of closets and tables should be balanced.3. A maximum of 95 should be manufactured from each product.If we model this problem as a linear programming problem and representC: number of closets to be manufacturedT: number of tables to be manufacturedO: number of office chairs to be manufactured And each closet set is sold for $400, each table set for $300 and each office chair for $80,Then, what number of each product should be manufactured to maximize the revenue? (Decimal numbers are OK)Q1.a (10 points) Suppose that Woodworks Industries Inc. decided to reduce the max production requirement for each item from 95 to 80. How would this assumption change the optimal solution and the objective function? Why?Q1.b. (10 points) Suppose that Woodworks Industries Inc. has decided not to accept decimals numbers for decision variables and has asked for integer (whole) values for decision variables. Does this assumption change the optimal solution? Why?.c (10 points) Suppose that Woodworks Industries Inc. decided NOT to impose the balance requirement constraint for tables and closets. How would this assumption change the optimal solution and the objective function? Why?

Exam 2 V. Review Time Matters Help QuickB File Home Insert Page Layout Formulas Data View % Cut Calibri - 11 - A A aD Wrap Text General Copy aste Format Painter BIU - - DA E Merge & Center - $ - % " Font Alignment Number Clipboard K26 X V fx A B C D .. E F G H K 2 Decision Variables Closets Tables Chairs Max production A W Min production req. 95 Obj. function: Profit $400 $300 $80 Constraints: LHS RHS 8 Mahogany 2.5 1.5 300 Pine 1 2 350 10 Carpenter 5 3