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# The Humane Society has asked for our help again this week. Currently they are charging $50 for an adoption fee. Unfortunately they just pulled this number out of the air and do not know why they are charging this amount. They would like to charge an amount that covers all the adoption costs – both the variable costs for adoptions as well as the fixed cost for the kennel portion of the Humane Shelter operations. We can help them by doing a breakeven analysis. During a client meeting we gathered these facts. There are 2 part-time employees that each earn$1000 per month. The utilities for the kennel area $water, electricity$ are $200 per month. The average food cost for animals in the kennel is$800 per month. In addition, each animal that is adopted receives a rabies vaccination that costs $4 and is micro-chipped that costs$6. At the current cost of $50, how many animals must be adopted to break-even? What would break-even be at a$60 adoption fee? What would break-even be if the fee were lowered to $40? The newspaper has suggested that the Humane Society advertise to increase pet adoptions. The package that they have recommended costs$1000 for a very small ad run every day for a month. If the Humane Society does this extra advertising, how will it affect breakeven? Based on what you have learned about elasticity, what price do you recommend for the adoption fee?

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## Answer to a math question The Humane Society has asked for our help again this week. Currently they are charging $50 for an adoption fee. Unfortunately they just pulled this number out of the air and do not know why they are charging this amount. They would like to charge an amount that covers all the adoption costs – both the variable costs for adoptions as well as the fixed cost for the kennel portion of the Humane Shelter operations. We can help them by doing a breakeven analysis. During a client meeting we gathered these facts. There are 2 part-time employees that each earn$1000 per month. The utilities for the kennel area $water, electricity$ are $200 per month. The average food cost for animals in the kennel is$800 per month. In addition, each animal that is adopted receives a rabies vaccination that costs $4 and is micro-chipped that costs$6. At the current cost of $50, how many animals must be adopted to break-even? What would break-even be at a$60 adoption fee? What would break-even be if the fee were lowered to $40? The newspaper has suggested that the Humane Society advertise to increase pet adoptions. The package that they have recommended costs$1000 for a very small ad run every day for a month. If the Humane Society does this extra advertising, how will it affect breakeven? Based on what you have learned about elasticity, what price do you recommend for the adoption fee?

Brice
4.8
To calculate the breakeven point for the adoption fee, we need to consider both the fixed costs $such as employee salaries and utilities$ and the variable costs $such as food, vaccinations, and microchipping$. Let's start by calculating the fixed costs: - Salaries for 2 part-time employees: $1000/month * 2 =$2000/month - Utilities for the kennel area: $200/month The total fixed costs per month are$2000 + $200 =$2200. Next, let's calculate the variable costs per animal adopted: - Food cost per month: $800/month - Rabies vaccination cost per animal:$4 - Microchipping cost per animal: $6 The total variable costs per animal adopted are$800 + $4 +$6 = $810. Now we can calculate the breakeven point for each adoption fee: 1. At the current cost of$50, the breakeven point can be calculated as: Breakeven point = Fixed costs / $Adoption fee - Variable costs per animal$ Breakeven point = $2200 / $$50 - $810$ =$2200 / -$760 = -2.89 Since the breakeven point is negative, it means that the Humane Society would need to adopt more than 2.89 animals to cover their costs. In this case, we can consider rounding up to 3 animals. 2. At a$60 adoption fee: Breakeven point = $2200 / $$60 - $810$ =$2200 / -$750 = -2.93 Again, rounding up, the breakeven point would be 3 animals. 3. At a$40 adoption fee: Breakeven point = $2200 / $$40 - $810$ =$2200 / -$770 = -2.86 Rounding up, the breakeven point would be 3 animals. 4. If the Humane Society does the extra advertising at a cost of$1000, it will increase the fixed costs. Let's assume this increases the fixed costs to $3200 per month. We can recalculate the breakeven point at the current$50 adoption fee: Breakeven point = $3200 / $$50 - $810$ =$3200 / -\$760 = -4.21 Rounding up, the breakeven point would be 5 animals. Based on what we have learned about elasticity, it is important to consider the demand for pet adoptions. If the demand is elastic, meaning that a small change in price will significantly affect the number of adoptions, it might be more beneficial to lower the adoption fee to increase the number of adoptions and potentially cover the costs. However, if the demand is inelastic, meaning that a change in price will not significantly affect the number of adoptions, it might be possible to increase the adoption fee to cover the costs without a significant decrease in adoptions. Without specific information about the elasticity of demand for pet adoptions in the area, it is difficult to recommend an exact adoption fee. However, it might be worth considering a price that is slightly higher than the current fee to better cover the costs, while also taking into account the affordability for potential adopters and the overall goal of finding suitable homes for the animals.
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