Question 4: [10 marks} A. carpenter makes tables and chairs. Each table can be sold for a prot of $13!? and each chair for a prot of $10. The carpenter can afford to spend up to 413 hours per week working and takes six hours to make a table and three hours to make a chair. Customer demand requires that he makes at least three times as many chairs as tables. Table5 take up four times as much storage space as chairs and there is room for at most four tables each week. Shipments of tables and chairs are only made at the end of the week. Let If he the number tables produced and, ac.- be the number of chairs produced. {i} Formulate the linear programming problem of how many of each product to produce to maximize prot. Clearly set up the objective function and constraints. [25 marks] {ii} Draw a graph with number of tables produced on the horizontal axis. Mark the feasible region clearly. Your graph MUST include one isoobjective line. [25 marks] (iii) What is the optimal level of prots and how many tables and chairs will give this level? [1.5 marks] (iv) The carpenter has been o'ered the chance to hire an extra room, thereby doubling the effective storage space. What is the maximum amount he would be prepared to pay [per week) for the hire of this storage room? Give a full explanation. [1.5 marks] (v) Instead of selling tables and chairs separately, the carpenter decides to only sell sets consisting of one table and four chairs. Find the number of sets that maximizes the carpenter's prots and compare the new prots to to the results in (iii). [2 marks]