Discuss your recommendation to the customer based on both mathematical reasoning and contextual details. Your discussion should include the following:
• How the algebraic evaluation and graph support the recommendation
• Any relevant contextual details that pertain to the recommendation (e.g., flexibility, distance, availability, etc.)
1. Discuss the different options and the customer’s needs.
This is what my answer is
Company A has a 10% discount for every dollar spent so the teacher only has to pay 90% of the price. This is shown in the graph with the blue curve.
Company B has a 20% discount for every dollar spent above $20, but there is no discount for anything under $20. This is shown in the graph with the red curve.
So when x is less than $40 company A’s curve is below company B’s curve so company A offers the better price for purchases below $40.
When x is greater than $40 company A’s curve is above company B’s curve so company B offers the better price for purchases above $40.
When x = 40 the curves intersect so at $40 the companies prices are the same.
The best choice for the teacher depends on the amount that he/she is going to spend. If it’s less than $40 the best choice is company A but if it’s more than $40 company B is the best choice.
Company A is y = .90x. So .90(40) is 36 so when x is less than 40 company A’s price is lower which is the better price for purchases.
Company B is y =x when x is less than or equal to $20. So 40 = 40. This is at the point when the company’s prices are the same.
Company B is y = .80x + 4. So .80(40) + 4 is 36. So at this point when the teacher is purchasing $40 or more company B is the better price.
So company A is the best selection for the teacher when making small purchases and company B is for larger purchases.
Teachers Response Back:
The solution point is appropriately referenced, but the discussion lacks a specific recommendation based on the needs of the hypothetical customer. Revise to provide such a recommendation.
The two cost options are appropriately reviewed, but remember to review the needs of the customer as well.
Not Sure what else they are looking for any Suggestions?
Based on the given information and the customer's needs, I would recommend the following:
For purchases under $40, it is recommended to choose Company A. This is because Company A offers a 10% discount for every dollar spent, resulting in a lower price compared to Company B. The algebraic evaluation supports this recommendation, as the equation y = 0.90x for Company A shows that the price is 90% of the total cost.
For purchases above $40, it is recommended to choose Company B. Although Company B does not offer a discount for purchases under $20, for purchases above $40, their 20% discount for every dollar spent above $20 provides a better price compared to Company A. The equation y = 0.80x + 4 represents Company B's pricing when x is greater than $40, which calculates to a lower price at $40 or more.
When the customer spends exactly $40, both companies offer the same price, as shown by the point where the two curves intersect on the graph.
In terms of contextual details, it is important to consider factors such as flexibility, distance, and availability. You may want to assess which company offers better flexibility in terms of returns or exchanges, as well as their proximity to the teacher. Additionally, considering the availability of the products or services required may also influence the final recommendation.
Based on this analysis, the recommendation is as follows: For purchases below $40, choose Company A for the better price. For purchases above $40, choose Company B for the better price. It is also recommended to consider the contextual details mentioned earlier to make a well-informed decision.
Based on the customer's needs, the recommendation should consider both the mathematical reasoning and the relevant contextual details.
In this case, the customer, who is a teacher, needs to decide between two companies, A and B, based on their pricing models. Company A offers a 10% discount for every dollar spent, while Company B offers a 20% discount for every dollar spent above $20, with no discount below $20. The customer's decision should be based on the total amount they plan to spend on their purchases.
To evaluate the options mathematically, we can use algebraic evaluation and the graph provided. The algebraic evaluations of the two companies' pricing models show that company A's equation is y = 0.90x and company B's equation is y = 0.80x + 4, where x is the total amount spent and y is the price paid.
By graphing the equations, we can visually see the intersection point at $40, where the prices of both companies are the same. Below $40, company A's curve (blue) is below company B's curve (red), indicating that company A offers a better price for purchases below $40. Above $40, company A's curve is above company B's curve, indicating that company B offers a better price for purchases above $40.
Considering the contextual details, it is important to note any relevant factors such as flexibility, distance, availability, or any other personal preferences. These factors may affect the customer's decision-making process. For example, if one company offers free shipping or has better customer service, these aspects should be taken into account as well.
Based on the mathematical reasoning and the contextual details, a specific recommendation can be made to the customer. For small purchases below $40, Company A would offer the better price. However, for larger purchases exceeding $40, Company B would be the better choice. The customer should consider their spending requirements and any additional factors that are important to them in order to make an informed decision.
It is important to highlight that this recommendation is based on the assumption that price is the primary factor for the customer. It is always recommended for the customer to consider other factors, such as quality, reputation, and customer service, before making a final decision.