ABC Widget company managers reached a consensus that expanding capacity provides a more favorable long$-$term solution for customer service. In this regard, the Baltimore plant only has the option to increase its capacity by $30,000$ units at a cost of $$20,000.$ Conversely, the St$.$ Louis and Kansas City plants have the option to increase the capacity by either $50,000$ or $100,000$ units, with the relevant cost details outlined below.Option $1-$ Increase the current capacity by $50,000$ units

Option $2-$ Increase the current capacity by $100,000$ units

While all customer demands must be met, each plant can have at most one option to increase its

capacity. Construct a mathematical model to assist your manager in determining the optimal

capacity expansion choice. Document your algebraic formulation in a worksheet with an objective

function, decision variables, and constraints. $(10$ pts$)$

e$)$ Solve the model you developed in d$)$ and answer the following questions.

i$.$ What$$s your new minimum total cost? $(15$ pts$)$

ii$.$ Create a row or column in excel to illustrate the demand fulfillment $(5$ pts$)$

iii. Createaroworcolumninexceltodemonstratethecapacityutilization$(5$pts$)$

iv$.$ Prepare a short statement to explain the results to your manager $(5$ pts$)$