The optimal production plan is to produce 500 Smart TVs and 0 LED TVs. This will maximize the company's profit.
How to solve
To determine the optimal production quantities for Smart TVs and LED TVs, we need to calculate the contribution margin per unit for each type of TV and compare it to the production constraints.
Smart TV:
Contribution margin per unit = Selling price - Variable cost per unit = $800 - $400 = $400
Production constraint = Demand = 500 units
LED TV:
Contribution margin per unit = Selling price - Variable cost per unit = $600 - $300 = $300
Production constraint = Demand = 700 units
Since the contribution margin per unit for Smart TVs ($400) is higher than that of LED TVs ($300), the company should prioritize producing Smart TVs.
However, they also need to consider the production constraints. The maximum number of Smart TVs they can produce is 500 units.
Therefore, the optimal production plan is to produce 500 Smart TVs and 0 LED TVs. This will maximize the company's profit.
The Complete Question
Suppose a television manufacturing company produces two types of TVs: Smart TVs and LED TVs. The company has updated its production costs, demand, and selling prices for each type of TV, as shown below:
Smart TV:
Selling price: $800
Variable cost per unit: $400
Fixed cost: $50,000
Demand: 500 units
LED TV:
Selling price: $600
Variable cost per unit: $300
Fixed cost: $40,000
Demand: 700 units
Given these updated details, how many Smart TVs and LED TVs should the company produce to maximize its profit?