1. Solve the following linear programming problem graphically: Minimise Z = 200 x + 500 y subject to the constraints: x + 2y 2 10 3x + 4y S 24 x 20, y 2o 2. A manufacturing company makes two types of television sets; one is black and white and the other is colour. The company has resources to make at most 300 sets a week. It takes Rs 1800 to make a black and white set and Rs 2700 to make a coloured set. The company can spend not more than Rs 648000 a week to make television sets. If it makes a profit of Rs 510 per black and white set and Rs 675 per coloured set, how many sets of each type should be produced so that the company has a maximum profit? Formulate this problem as a LPP given that the objective is to maximise the profit. 3. A dietician wishes to mix two types of foods in such a way that vitamin contents of the mixture contain atleast 8 units of vitamin A and 10 units of vitamin C. Food T contains 2 units/kg of vitamin A and 1 unit/kg of vitamin C. Food Ir contains 1 unit/kg of vitamin A and 2 units/kg of vitamin C. It costs Rs 50 per kg to purchase Food T and Rs 70 per kg to purchase Food 'II'. Formulate this problem as a linear programming problem to minimise the cost of such a mixture. 4. A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftsman's time in its making while a cricket bat takes 3 hours of machine time and 1 hour of craftsman's time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman's time. (1) What number of rackets and bats must be made if the factory is to work at full capacity? (ii) If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity. 5. There are two projects of $100,000 each which are expected to generate the following cash inflows in six years: PROJECT A Year 1: $20,000 Year 2: $15,000 Year 3: $30,000 Year 4: $35,000 Year 5: $30,000 Year 6: $25,000 PROJECT B $80000 $10000 $5000 $5000 $10000 $15000 Required: Compute payback period of the PROJECTS. Should the investment be made if management wants to recover the initial investment in 4 years or less? Which project you will choose and why? 6. Two project requires an initial investment of $100,000 each and are expected to generate the following net cash inflows: PROJECT A PROJECT B Year 1: $45,000 30,000 Year 2: $70,000 30,000 30,000 Year 3: $50,000 Year 4: $45,000 30,000 Year 5: $40,000 30,000 Required: Compute net present value and Profitability Index and the IRR of the projects and rank the projects if the minimum desired rate of return is 10%