3. [10 marks] For the following problem, (i) formulate, (ii) solve graphically by sketching the constraints and a few constant profit lines, (iii) solve by hand using the Simplex Tableau. A houseware manufacturer produces two products: Drapes at a profit of $0.80 each and tablecloths at a profit of $1.00 each. Market limits dictate that tablecloths should be manufactured at a rate of no more than 12 per day. The manufacturer has a total of 16 hours of manufacturing labour available per day. Each tablecloth requires 1 hour of labour and each drape requires 0.5 hours of labour. Each drape requires 2 m2 of fabric to manufacture, and each tablecloth requires 1 m of fabric. The supply of fabric is limited to 40 m2 per day. At what rate should the manufacturer make each product to maximize the profit rate