Real grocery store is now considering adding a new refrigerator to its dairy products section,

which will include only Italian cheeses. There are five well$-$known Italian cheese types that can

be included in this new product assortment: grana padano, mascarpone, ricotta, mozeralla, and

gorgonzola. The refrigerator capacity is $350lt.$ Each pack of the cheese requires a certain space,

which changes according to cheese type. Also, the unit profit of a cheese pack in the

assortment is different for each type. If a cheese type is included in the assortment, there is a

fixed cost of dealing with the supplier and ordering independent of the number of packs stored.

For mascarpone, ricotta, and mozeralla cheeses, the supplier has minimum delivery amounts,

such that if any of these cheeses are kept in the assortment, at least the minimum numbers

should be bought. On the other hand, for grana padano, at least $40$ packs should be kept if

mascarpone cheese is not included in the assortment. Otherwise, there is no minimum amount.

The detailed information about pack sizes, profits, fixed costs, and minimum pack numbers can

be found in the below table.

Now, the dairy section manager of Real needs your help to solve her assortment problem. Can

you help her to find out which Italian cheese types and in what amounts should be kept in the

new refrigerator to get the maximum profit?