please do question 4

3. (25 marks) A company needs to rent space for its office employees, some of whom are physically challenged and therefore need to work in an accessible environment (no stairs, handrails on the walls, etc.). Space is available in Location 1 at a rate of $460 per square metre (per annum), while at Location 2 space rents for $900 per square metre (per annum). At location 1, only 30% of the space is accessible, while at location 2, 60% of the space is accessible. The company needs a total of at least 600 square metres of space, of which at least 300 square metres must be accessible. No more than 70% of the entire space rented is to be at Location 1, and no more than 80% of the entire space rented is to be at Location 2. (a) Formulate a linear optimization model for this situation. Write every constraint in standard form ( a number), with a one or two word description of the purpose of the constraint. (b) Without plotting any points outside the 750 by 750 region on the graph paper found on page 5, solve the model, clearly indicating each constraint with a word description next to it, the feasible region, the trial and optimal isovalue lines, and the point of optimality. Compute the exact solution algebraically, and clearly state the recommendation and the OFV. 4. (25 marks) An assembly plant for high-definition televisions makes two types of TVs. Model X is aimed at the price-sensitive market and has a net value (i.e. after subtracting all variable costs) when leaving the plant of S150 per television. Model Y is 4K with many more features; its net value is $450 per television. Each Model X requires 6 labour-hours in assembly-line 1, and 4 labour-hours in assembly-line 2. Each Model Y requires two labour-hours in assembly-line I, and 7.5 labour-hours in assembly-line 2. Each week assembly-line 1 is available for 6600 labour-hours, and assembly-line 2 is available for 8930 labour-hours. At least 40% of the total production must be of Model Y; however, they cannot sell more than 940 units of Model Y. (a) Formulate a linear optimization model for this situation. Write every constraint in standard form (S. = or > a number), with a one or two word description of the purpose of the constraint. (b) Without plotting any points outside the 1500 by 1500 region on the graph paper found on page 6, solve the model, clearly indicating each constraint with a word description next to it, the feasible region, the trial and optimal isovalue lines, and the point of optimality. Compute the exact solution algebraically, and clearly state the recommendation and the OFV. For question 4. 1500 Model Y 1000 500 500 1000 1500 Model X