Abernathy & Barnaby Woodworks Ltd. (A&B) makes tables and chairs from 30-inch-wide mahogany sheets that it purchases by the linear foot. It can purchase whatever mahogany it desires for $10 per linear foot up to 2250 linear feet per week. Each table requires 9 linear feet and each chair 3 linear feet (including waste). Each chair also utilizes a soft cushion. Up to 500 cushions can be purchased each week for $25 each. Other required hardware (supports, braces, nuts, bolts, etc.) averages $45 for each table and $25 for each chair. A&B sells the tables to retailers, for $300 each and each chair for $150 each. The 10 craftsmen employed by A&B are salaried workers. Their wages of $800 each per week as well as the $5000 per week in rent, insurance and utility costs are all considered fixed costs. To produce a table requires 1 hour of a craftsmen's time, whereas each chair requires only 36 minutes. Each craftsman averages 37.5 productive work hours per week. Abernathy Barnaby Woodworks Ltd. policy mandates that the ratio of chairs to tables must be between 4 to 1 and 6 to 1. Required: a. Develop a linear programming model for A&B. The objective function should maximize its gross weekly profit (gross revenue less the variable costs of wood, cushions and other materials). Express the feasible region by the nonnegativity constraints and a set of five functional constraints (wood and cushion availability, the minimum and maximum chair to table ratios, and the maximum weekly production time). b. Solve for A&B's optimal weekly production schedule of tables and chairs. What is the optimal gross weekly profit? What is the optimal net weekly profit (gross weekly profit less the fixed labor, rent, insurance and utility costs)? c. From the Solver reports, determine and interpret the shadow prices for: i) linear feet of mahogany wood ii) cushions iii) production hours Question 02 (10 points) Sean OHurley is a farmer from Wellington County, Ontario with 250 acres on which he wishes to plant wheat and corn to maximize his expected return for the season. For crop rotation purposes he must plant at least 50 acres of each crop. He can participate in an Ontario provincial government agricultural program that will require him to produce at least as much wheat as corn. Under this Ontario provincial program, he is guaranteed to earn $150 per acre of wheat planted and $200 per acre of corn planted. Alternatively, he can opt not to participate in the program, in which case he projects he would make only $125 per acre of wheat planted and $184 per acre of corn planted. Required: Formulate and solve in Excel using Solver. On the basis of your LP analysis what would you recommend to Sean?