The Vandelay furniture company makes bookshelves and tables.Consider the following Linear Programming Model:          X1 = the number of bookshelves made in a day.          X2 = the number of tables made in a day.          Maximize:  Z = 50X1 +50X2       Profit  ($)          Subject to:                   20X1 + 11X2 <= 100          Labor  (hours)                   7.1X1 + 10X2 <= 50            Lumber  (board-feet)What's the lowest profit on a bookshelf can be, without changing the optimal solution?Another way to ask this is, what's the lower bound on the sensitivity range for C1?(Round your answer to 1 decimal place.)

A craft furniture manufacturer produces round kitchen tables (X1) and matching chairs (X2) in its workshop from 600 board feet of oak.  Each table requires 30 hours of labor and each chair requires 18 hours, and there are 480 hours of labor available.  Each table requires 40 board feet and each chair requires 15 board feet.  A table provides $575 in profit and each chair provides $120 in profit.  In the integer programming model formulation for this problem, if each table requires 6 chairs to go with it, but additional chairs can be made and sold separately, this constraint, in proper form for computer solution, could be written as:Group of answer choices6X1 + X2  0X1 + 6X2  06X1 – X2  0X1 + X2 6

The Woodworks Company produces a variety of custom-designed wood furniture, made from either cherry or oak. The company knows that wood prices and labor costs are likely to increase in the future. The table below shows the number of board-feet and labor hours required for a bookshelf, the current costs per board-foot and labor hour, and the anticipated annual increases in these costs.Build a spreadsheet model that enables the company to experiment with the growth rates in wood and labor costs so that a manager can see, both numerically and graphically, how the costs of bookshelves vary in the next few years.ResourceCherryOakLaborRequired per Bookshelf303016Current Unit Cost$5.50$4.30$18.50Anticipated Annual Cost Increase2.40%1.70%1.50%

The logistics/operations manager of a mail order house purchases two products for resale: King Beds (K) and Queen Beds (Q). Each King Bed costs $500 and requires 100 cubic feet of storage space, and each Queen Bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each King Bed is $300, and for each Queen Bed is $150. What is the objective function?Multiple ChoiceZ = $150K + $300QZ = $500K + $300QZ = $300K + $500QZ = $300K + $150QZ = $100K + $90Q

Instructions: Use the given information to answer the questions and interpret key features. Use any method of graphing or solving.The roots of the quadratic function describing the relationship between number of products produced and overall profit margin are x=0𝑥=0 and 100100. The vertex is (50,1000)(50,1000).The maximum profit of $$ dollars is reached when items are produced.The first root tells us that the profit will be 00 when products are produced. The second root says once items are made, the company is no longer making any profit. (They do not have production capacity and have to outsource for anything over 5050.)

Instructions: Use the given information to answer the questions and interpret key features. Use any method of graphing or solving.The roots of the quadratic function describing the relationship between number of products produced and overall profit margin are x=0𝑥=0 and 2828. The vertex is a minimum at (14,−40)(14,−40).The company actually loses money on their first few products as it costs them more to make them, but once they hit items they break even again.The worst case scenario is that they produce items, as they will have a profit of dollars. The first root tells us that the profit will be 00 when products are sold.