Question 1: A material is required for the interior wall of electric air-furnace capable of temperatures up to 1275 K. Think out what attributes a material must have if it is to be made into windings and function properly in a furnace. List the function and the constraints; set the objective to "minimize cost" and the free variables to "choice of material".

Question 2: The standard CD ("Jewel" case) cracks easily and, if broken, can scratch the CD. Jewel cases are made of injection molded polystyrene, chosen because it is transparent, cheap and easy to mold. A material is sought to make CD cases that do not crack so easily. The case must still be transparent, able to be injection molded, and able to compete with polystyrene in cost. List the function and the constraints; set the objective to "minimize cost" and the free variables to "choice of material".

Question3: Material index for a light, strong beam (Figure 1). In stiffness-limited applications, it is elastic deflection that is the active constraint: it limits performance. In strength-3, limited applications, deflection is acceptable provided the component does not fail; strength is the active constraint. Derive the material index for selecting materials for a beam of length L, specified strength and minimum weight. 

For simplicity, assume the beam to have a solid square cross-section t x t. You will need the equation for the failure load of a beam. It is

Where ym is the distance between the neutral axis of the beam and its outer filament and I = t4/12 = A2/12 is the second moment of the cross-section.