Allstate HVAC recently developed a low-end electronic thermostat that it plans on selling via a cable channel marketing program.The cable program's fee for selling the item is 20% of revenue.For this fee, the program will advertise the thermostat over six 10-minute segments in September.Allstate's fixed costs of producing the thermostats are $110,000 per production run.The company plans to wait for all orders to come in, and then it will produce exactly the number of units ordered.Variable production costs are $25 per unit.In addition, it will cost approximately $5 per unit to ship the thermostats to customers.Production time will be less than three weeks.Henry Kristen, a product manager at Allstate, is charged with recommending a price for the thermostat.Based on his experience with similar items, focus group responses, and survey information, he has estimated the number of units that can be sold at various prices: $$\begin{array} { c c }
\text { Unit Price } & \text { Quantity } \
\hline \$ 74.99 & 15,000 \
\$ 63.99 & 20,000 \
\$ 54.99 & 25,000 \
\$ 49.99 & 35,000
\end{array}$$ At what price is profit maximized?

Question

Allstate HVAC recently developed a low-end electronic thermostat that it plans on selling via a cable channel marketing program.The cable program's fee for selling the item is 20% of revenue.For this fee, the program will advertise the thermostat over six 10-minute segments in September.Allstate's fixed costs of producing the thermostats are $110,000 per production run.The company plans to wait for all orders to come in, and then it will produce exactly the number of units ordered.Variable production costs are $25 per unit.In addition, it will cost approximately $5 per unit to ship the thermostats to customers.Production time will be less than three weeks.Henry Kristen, a product manager at Allstate, is charged with recommending a price for the thermostat.Based on his experience with similar items, focus group responses, and survey information, he has estimated the number of units that can be sold at various prices: $$\begin{array} { c c } 
\text { Unit Price } & \text { Quantity } \
\hline \$ 74.99 & 15,000 \
\$ 63.99 & 20,000 \
\$ 54.99 & 25,000 \
\$ 49.99 & 35,000
\end{array}$$ At what price is profit maximized?

Quizplus · Accepted Answer

To maximize profit, we need to calculate the profit at each price point. Profit is calculated as (Price - Variable Costs) * Quantity - Fixed Costs - Cable Fee. The variable costs include production and shipping costs, which total $30 ($25 + $5) per unit. The cable fee is 20% of revenue (Price * Quantity).1. At $74.99:   - Revenue = $74.99 * 15,000 = $1,124,850   - Variable Costs = $30 * 15,000 = $450,000   - Cable Fee = 20% of $1,124,850 = $224,970   - Profit = $1,124,850 - $450,000 - $224,970 - $110,000 = $339,8802. At $63.99:   - Revenue = $63.99 * 20,000 = $1,279,800   - Variable Costs = $30 * 20,000 = $600,000   - Cable Fee = 20% of $1,279,800 = $255,960   - Profit = $1,279,800 - $600,000 - $255,960 - $110,000 = $313,8403. At $54.99:   - Revenue = $54.99 * 25,000 = $1,374,750   - Variable Costs = $30 * 25,000 = $750,000   - Cable Fee = 20% of $1,374,750 = $274,950   - Profit = $1,374,750 - $750,000 - $274,950 - $110,000 = $239,8004. At $49.99:   - Revenue = $49.99 * 35,000 = $1,749,650   - Variable Costs = $30 * 35,000 = $1,050,000   - Cable Fee = 20% of $1,749,650 = $349,930   - Profit = $1,749,650 - $1,050,000 - $349,930 - $110,000 = $239,720The highest profit is achieved at a price of $74.99.

Allstate HVAC Recently Developed a Low-End Electronic Thermostat That It