Question $1(25$ Points$)$ Determine the best production quantity to minimize cost. Complete the formulation of a LP model and run Solver. Enter answers to the following questions in the corresponding answer boxes.$1)(3$ Points$)$ How many decision variables are there in this problem? $82)(3$ Points$)$ How many contraints are there in this problem? $63)(3$ Points$)$ What is the value of the objective function? $$$$33,288\mathrm{.}004)(8$ Points$)$ Identify the production plan for each product by month. Production Plan January February March April GOLD$3$A $12772231915635$ GOLD$3$B $100025227817005)(2$ points$)$ Run a sensitivity report.$$ If the inventory requirement for part GOLD$3$A in April increased by $1,$ how would the total cost change? $$$$-($enter a dollar ammount here to two decimal places$)$ Questions $6,7$ and $8$ please update the original model. These are non$-$cumulative $-$ update the original model for each question. $6)(2$ points$)$ You hear back from one of the retired employees and it turns out that he is not available to work in January, but can work February through April. How much does this change $($increase$)$ the total cost? $$$$(843\mathrm{.}22)($enter a dollar ammount here to two decimal places$)7)(2$ points$)$ More bad news, accounting underestimated the production cost increase in March and April and are now estimating a $25\%$ increase.$$ With the $25\%$ increase, what is the Total Cost? $$$$34,888\mathrm{.}44($enter a dollar ammount here to two decimal places$)8)(2$ points$)$ You have a total budget of $$75,000$ and need to reduce the total cost.$$ The only constraints that you can change are the inventories at the end of April. By eliminating these constraints will you be within your budget? Yes