A manufacturing company, called Vista, produces three products A$,$ B$,$ and C$.$ The labour and

material resources required to produce them are shown in Table $1.$ For example, producing $1$

kg of product A requires $2$ units of labour and $1$ unit of material. The company has $91\mathrm{.}5$ units

of labour and $49\mathrm{.}5$ units of material available daily. According to market demand, the company

stipulates the maximum and minimum daily production volume of each product as shown in

Table $2.$ E$.$g$.,$ for product A$,$ the company needs to produce between $5$ kg and $32$ kg per day.

Product A is the company$$s main product, so the company emphasises that in terms of daily

production volume, product A must account for at least $80\%$ of all products.

The company wants to maximise its profit. Profits for products B and C are $$15/$kg and $$20/$kg$,$

respectively. Product A is sensitive to an uncontrollable environmental factor which has two

possible states, i$.$e$.,$ S$1$ and S$2.$ Product A$$s profit in those two possible states is $$5/$kg and

$$15/$kg$,$ respectively.

Table $1.$ Labour and material requirements

Units of resources required per kg of product

Product Labour Material

A $21$

B $32$

C $53$

Table $2.$ Daily production limits

Product Maximum $($kg$)$ Minimum $($kg$)$

A $325$

B $203$

C $102$

By analysing historical data, you find that both states of the environmental factor are

equally likely to occur. Determine the production plan that maximises the expected

value $($EV$)$ of total daily profit, by formulating a linear programming $($LP$)$ problem and

solving it using Excel Solver. For the Excel Solver part, please paste here one

screenshot: the problem worksheet just before clicking the Solver command. That is$,$

after developing the Excel Solver model, press Ctrl $+$ ~ $($tilde$)$ to show formulas in

cells, and then take a screenshot with row and column headings.

Please limit the answer to within one $(1)$ page.