How do I maximize the following equation:
$ 150 \le 9.05x + 18.89y \\ \text{constraints: } \\ x > 0, y > 0 \\ \text{$x$ and $y$ must be whole numbers.} $
I cannot use calculus to solve this question, which would have been easy if I could.
The student council is planning a school dance. There will be an opportunity for students to purchase refreshments. The council is going to sell chocolate bars but also wants to offer snacks to students who do not like chocolate bars (or who may have food allergies!)
Ashley, a member of the student council, researched prices at two stores.
She found 3 types of non-chocolate bars, Zagnut, Zero and PayDay. The prices of boxes of the bars at two different stores are shown below:$\begin{array}{c|c} \text{COSCO}&\text{WALMART}\\ \hline \text{Box of }24\text{ Zagnut bars: }\$12.49&\text{Box of }18\text{ Zagnut bars: }\$9.05\\ \text{Box of }18\text{ Zero bars: }\$9.89&\text{Box of }12\text{ Zero bars: }\$6.69\\ \text{Box of }36\text{ PayDay bars: }\$18.89&\text{Box of }6\text{ PayDay bars: }\$4.45 \end{array}$
The student council has $\$150 cash available for the initial purchase of these non-chocolate bars. They want to offer at least two types of the non-chocolate bars for the students to purchase at the dance.
Your job is to:
- decide which bars the student council should purchase and from where to purchase them. You must purchase at least two types of bars (or all 3)
- fill in the shopping list provided, clearly indicating your choice of bar and quantity.
- set the price for the sale of the bars at the dance knowing that the Student Council must make a profit of at least \$200$.
- Justify the choices that you make to solve the problem