Linear systems of equations and inequalities are used widely in the fields of business and
economics to maximize profit, minimize cost, and balance the production and consumption of
goods. In fact, there are entire careers in Production and Operations Management that are built
around this skill.
Solve each problem in order and save your work as you progress as you will create a
professional presentation in the end.
Defining the Quantities: The Golden Nut specialty store has obtained 60 lbs. of cashews
and 50 lbs. of premium almonds at a good price from its supplier. Since the almonds are
more expensive and more of a delicacy than the cashews, it is better to sell the cashews
mixed with almonds in order to get a better price for them. The storeowner decides to
sell two products: Hearty Nut Mix and Premium Blend.
1. If each pound of Hearty Nut Mix contains 4 ounces of almonds and 12 ounces of
cashews, write an expression that represents the number of pounds of each nut in x
pounds of the mix. [Hint: What fraction of the pound is cashews, and what fraction is
2. If each pound of Premium Blend contains 8 ounces of almonds and 8 ounces of
cashews, write an expression that represents the number of pounds of each nut in y
pounds of the mix.
3. Complete the following table and use it to write an expression that represents the
total number of pounds of cashews used for both mixes together. Then, write an
expression for the total number of almonds used for both mixes together.
Type of Mix No. Of Pounds of
No. of Pounds of
No. Of Pounds
Hearty Nut Mix x
Premium Blend y
4. Finally, your market research shows that since the Premium Blend is much more
popular, you can afford to charge quite a bit more for it, obtaining a profit of $0.45 per
pound for it while you can only earn a profit of $0.30 per pound for the Hearty Nut
Mix. Write an expression for the amount of profit that you would make from selling x
pounds of Hearty Nut Mix and y pounds of Premium Blend.
These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.
1. If each pound of Hearty Nut Mix contains 4 ounces of almonds and 12 ounces of cashews, write an expression that represents the number of pounds of each nut in x pounds of the mix. [Hint: What fraction of the pound is cashews, and what fraction is almonds?]
According to the problem, Hearty Nut Mix contains 4 ounces of almonds and 12 ounces of cashews. Thus 1 pound Mix contain 4/16 = 0.25 pound of almonds and 12/16 =0.75 pounds of Cashews. This x pounds of Mix contain 0.25x of almonds and 0.75x pounds of Cashews....