Question #$3$:

$T{J}^{\text{'}}s,$ Inc., makes three nut mixes for sale to grocery chains located in the Southeast. The three mixes, referred to as the Regular Mix, the Deluxe Mix, and the Holiday Mix, are made by mixing different percentages of five types of nuts.

In preparation for the fall season, $T{J}^{\text{'}}s$ has just purchased the following shipments of nuts:

$\backslash$table$[[$Type of Nut,Shipment Amount $($pounds$)],[$Almond$,6000],[$Brazil$,7500],[$Filbert$,7500],[$Pecan$,6000],[$Walnut$,7500]]$

The Regular Mix consists of $15\%$ almonds, $25\%$ Brazil nuts, $25\%$ filberts, $10\%$ pecans, and $25\%$ walnuts. The Deluxe Mix consists of $20\%$ of each type of nut, and the Holiday Mix consists of $25\%$ almonds, $15\%$ Brazil nuts, $15\%$ filberts, $25\%$ pecans, and $20\%$ walnuts.

TJ$\text{'}$s accountant analyzed the cost of packaging materials, sales price per pound, and so forth, and determined that the profit contribution per pound is $$1\mathrm{.}65$ for the Regular Mix, $$2\mathrm{.}00$ for the Deluxe Mix, and $$2\mathrm{.}25$ for the Holiday Mix.

Customer orders already received are summarized here:

$\backslash$table$[[$Type of Mix,Order $($pounds$)],[$Regular$,10,000],[$Deluxe$,3,000],[$Holiday$,5,000]]$

Because demand is running high, it is expected that $TJ\text{'}$s will receive many more orders than can be satisfied. TJ$\text{'}$s is committed to using the available nuts to maximize profit over the fall season; nuts not used will be given to a local charity. Even if it is not profitable to do so$,$ TJ$\text{'}$s president indicated that the orders already received must be satisfied.

Summarize the model in algebraic form by defining the decision variables, the objective function and all the constraints. Type in microsoft please