Bakshi $10\mathrm{.}4$: Five life cycle modules involved in washing a cup in a standard size residential dish washer are shown in Figure $10\mathrm{.}14.$ For simplicity, many operations, emissions, and resources are not included, and flows are reported with only $1$ to $2$ significant figures. The utility mix $(75\%$ coal, $25\%$ natural gas$)$ is somewhat arbitrary, while a $10\%$ loss in transmission and distribution is typical.

a$.$ Write the technology and intervention matrices for the life cycle of a glass cup.

b$.$ Assuming that a single glass cup is used $800$ times, determine the corresponding nal demand, and calculate the life cycle emissions. Determine the scaling vector and draw the corresponding life cycle network diagram. You may assume that one dishwasher load is $80$ cups.