Example $5$: A usage$/$supply problem

"A conference organizer has to cater for lunches for the $5$ days of a conference. The organizer is faced with the problem of deciding on the daily supply of clean serviettes. The organizer knows that the number of conference attendees requiring lunch for the $5$ days are $130,220,180,120,$ and $100.$ The alternatives are

to buy new serviettes at $25$ a piece, or

to send used serviettes to the laundry where they can receive either a $48$ h service at $10$ a serviette, or a $24$ h service at $15$ a serviette.

If this conference is a once$-$off activity with respect to the provision of serviettes, how should the organiser provide serviettes to minimize the total cost?"

The problem is to manage serviettes for a $5$ day conference's lunches at minimum possible cost. This problem requires some additional work in defining the variables and setting up the objective and constraint functions. In this problem, the options of using serviettes in any $1$ day a

$*$Buy new serviettes

$*$Receive used serviettes from cleaning cleaning and$/$or$,*48$ h cleaning$),$

$*$Send used serviettes for cleaning cleaning and$/$or$,**48h$ cleaning$),$

$*$Store used serviettes$-$do not send for cleaning now.

Assume that there is no serviette in stock at the beginning of day $1.$

Example $4\mathrm{.}4$: An oil blending problem

"A multinational oil supplier produces two grades of gasoline, $U($unleaded$)$ and L $($leaded$),$ which it sells for $$1\mathrm{.}10$ and $$1\mathrm{.}00$ per liter, respectively. The refinery can buy three different types of refined oil, from three different sources, with the following constituents and prices:

$\backslash$table$[[\backslash$table$[[$Refined$],[$Oil$]],$Constituents,$],[,$A$,$B$,$C$,$Price $\frac{?}{L}$