4. A company imports electronic components that are used to assemble two different models of personal computers. One model, A, generates a profit contribution of €50 per unit while the other, B, generates a profit contribution of €40 per unit. For next week's production a maximum of 150 hours of assembly time can be made available. Each unit of A requires three hours of assembly time and each unit of B requires five hours. In addition the company currently has in inventory 20 display units used in B; thus no more than 20 units of B can be assembled. Finally, only 300 square metres of warehouse space can be made available next week for new production of these products. Each unit of A requires eight square metres and each unit of B requires five square metres. (i) Formulate this as a linear programming problem to find the optimal production schedule for next week. (ii) Find the solution to (i) using LINDO program. (iii) State the values and interpret the meaning of the dual variables using LINDO sensitivity analysis. (iv) Find the range of values for the profit contributions with which the current solution will remain optimal (v) Find the range of values within which the maximum number of assembly hours available must lie in order for the value of the appropriate dual variable found in (iii) to remain optimal.