optimization and modelling
a. With respecting to modeling of Optimization problem, briefly explain ANY TWO of the [6] following: d. A furniture manufacturer employs 6 skilled and 11 semiskilled workers and produces two [6] products: study table and computer table. A study table requires 2h of a skilled worker and 2 h of an unskilled worker. A computer table requires 2h of a skilled worker and 5h of an unskilled worker. As per the industrial laws, no one is allowed to work for more than 38h a week. The manufacturer can sell as many tables as he can produce. If the profit for a study table is R100 and for a computer table R160, how many study and computer tables should the manufacturer produce in a week in order to maximize the overall profit? Formulate this as a linear programming model. e. Consider Problem 2(d) above. Suppose that the demands of the study and computer tables are at least 40 and 45 , respectively, and the manufacturer pays R900 and R600 per week for each skilled and unskilled worker, respectively. If the manufacturer intends to fulfil the demand in full, what objective function would you suggest to the manufacturer's production planning problem? Justify your suggestion and formulate the problem as a linear programming model. f. A food production and retail chain is considering several projects that have varying capital requirements over the next 3 years. The projects are (1) possible plant expansion, (2) possible warehouse expansion, (3) possible addition of a transport unit, and (4) possible purchase of new machinery. The estimated net present value for each project, the investment requirements, and the available capital over the next 3 years are shown below. All figures are in million dollars. The main question is: which projects the company should choose in order to maximize the total net present value? Formulate the above problem as optimization problem. a. With respecting to modeling of Optimization problem, briefly explain ANY TWO of the [6] following: d. A furniture manufacturer employs 6 skilled and 11 semiskilled workers and produces two [6] products: study table and computer table. A study table requires 2h of a skilled worker and 2 h of an unskilled worker. A computer table requires 2h of a skilled worker and 5h of an unskilled worker. As per the industrial laws, no one is allowed to work for more than 38h a week. The manufacturer can sell as many tables as he can produce. If the profit for a study table is R100 and for a computer table R160, how many study and computer tables should the manufacturer produce in a week in order to maximize the overall profit? Formulate this as a linear programming model. e. Consider Problem 2(d) above. Suppose that the demands of the study and computer tables are at least 40 and 45 , respectively, and the manufacturer pays R900 and R600 per week for each skilled and unskilled worker, respectively. If the manufacturer intends to fulfil the demand in full, what objective function would you suggest to the manufacturer's production planning problem? Justify your suggestion and formulate the problem as a linear programming model. f. A food production and retail chain is considering several projects that have varying capital requirements over the next 3 years. The projects are (1) possible plant expansion, (2) possible warehouse expansion, (3) possible addition of a transport unit, and (4) possible purchase of new machinery. The estimated net present value for each project, the investment requirements, and the available capital over the next 3 years are shown below. All figures are in million dollars. The main question is: which projects the company should choose in order to maximize the total net present value? Formulate the above problem as optimization
