A store sells two types of nut mixtures. The standard mix contains 100 grams of cashews and 200 grams of peanuts and sells for $2. The deluxe mix contains 120 grams of cashews and 40 grams of peanuts and sells for $2.50. The store has 15kilograms of cashews and 20 kilograms of peanuts available. Based on past sales it needs to have at least as many standards as deluxe packages available. Represent algebraically (ie with equations and/or inequalities using defined variables) and geometrically (ie with a graph) the set of possible combinations of standard and deluxe packages the store could make.

Can someone help me with this question? I'm honestly confused because my teacher showed it to my class but I didn't understand.

1 answer

Let s and d be how many standard and deluxe packages
Let c and d be the amounts of cashews and peanuts

Now figure how many grams of each nut will be needed for the packages
120s + 120d <= 15000
200s + 40d <= 20000
s >= d

You did not ask, but I assume you want to maximize revenue.
Try using this in your linear algebra methods.