Question 2 Consider a ready-to-use broth product (900 mL) packaged in the TetraBrik carton with a dimension of L x W x H. The unfolded paperboard blank of the carton with scores lines is shown below. The shaded regions represent seal aps required for forming the carton. We are interested to calculate the dimensions of the carton that provide a minimal packaging material usage. (i) If W and S are 5.8 cm and 0.8 cm, respectively, determine the dimensions of L and H that would result in the smallest area, assuming cuboid package geometry and a headspace volume of 60 mL. Hint: write an equation area of the unfolded carton as a function of L; create a scatter (X-Y) plot of area versus L; determine the L value when the area is the smallest. (30%) (ii) From a teardown analysis of an actual carton package of a commercial product, the L x W x H dimensions are 8.9 cm, 5.8 cm, and 19.4 cm, respectively. Calculate the surface area (remember to include the seal aps) based on these dimensions and comment on whether the commercial package is optimized in terms of paperboard utilization. Justify your answer. (10 '70). I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I \ r I I \ a I \ I ' r I \ , I I \ , I ' r . ' , W/Z ' w ' ' 'x ' \ I x I \' I I I \\