A company makes and sells product X and product Y. Twice asmany units of product Y are made and sold as that of product X. Eachunit of product X makes a contribution of $10 and each unit of productY makes a contribution of $4. Fixed costs are $90,000.What is the total number of units which must be made and sold tomake a profit of $45,000?a. 7,500b. 22,500c. 15,000d. 16,875
Question
A company makes and sells product X and product Y. Twice asmany units of product Y are made and sold as that of product X. Eachunit of product X makes a contribution of 4. Fixed costs are 45,000?a. 7,500b. 22,500c. 15,000d. 16,875
Solution
To solve this problem, we first need to understand the profit equation. Profit is calculated as total revenue minus total costs. In this case, the total revenue comes from the sales of product X and product Y, and the total costs are the fixed costs.
Let's denote the number of units of product X sold as x. Since twice as many units of product Y are sold, we denote the number of units of product Y sold as 2x.
The contribution from each unit of product X to the total revenue is 4. Therefore, the total revenue (R) can be calculated as:
R = 10x + 4*2x = 10x + 8x = 18x
The profit (P) is calculated as total revenue minus total costs. We know that the company wants to make a profit of 90,000. Therefore, we can set up the following equation:
P = R - C 45,000 = 18x - 90,000
Solving this equation for x gives:
45,000 + 90,000 = 18x 135,000 = 18x
x = 135,000 / 18 x = 7,500
Therefore, the company needs to sell 7,500 units of product X. Since twice as many units of product Y are sold, the company needs to sell 2*7,500 = 15,000 units of product Y.
So, the total number of units which must be made and sold to make a profit of $45,000 is 7,500 + 15,000 = 22,500 units.
So, the correct answer is b. 22,500.
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