$[20$ points$]$ Hot Dee is a hot sauce producer. The demand forecast for the next four weeks, unit production, and inventory holding costs are given in the table below. Currently, there are $500$ bottles on$-$hand. Due to the contract obligations, no shortages are allowed. At the end of the $4^{th}$ week, the on$-$hand inventory must be more than $400$ units.

$\backslash$table$[[$Week$,$Demand Forecast,Unit Production Cost $($$$),$Unit Inventory Holding Cost $($$$)],[1,2800,5\mathrm{.}00,0\mathrm{.}10],[2,3400,5\mathrm{.}25,0\mathrm{.}12],[3,3600,5\mathrm{.}50,0\mathrm{.}12],[4,2900,4\mathrm{.}95,0\mathrm{.}10]]$

MGMT $3106$: Management Science and Operations Management

a$.$ Use the level production strategy. What is a good production level? What is the total cost? $($Production $+$ Inventory holding$).$ Show all work. $($Hint: You may need to consider the net demand for each week$).$

b$.$ Use the chase demand production strategy. What is the production level for each week? What is the total cost? Show all work. $($Hint: You may need to consider the net demand for each week$).$

c$.$ Use the minimum cost strategy $($optimization with linear programming$).$ What is the production level for each week? What is the total cost? Show all work including Excel Solver parameters or LPSolve model.