.A company makes and sells product X and product Y. Twice as manyunits of product Y are made and sold as that of product X. Each unit ofproduct X makes a contribution of $10 and each unit of product Y makes acontribution 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?e. 7,500f. 22,500g. 15,000h. 16,875
Question
.A company makes and sells product X and product Y. Twice as manyunits of product Y are made and sold as that of product X. Each unit ofproduct X makes a contribution of 4. Fixed costs are 45,000?e. 7,500f. 22,500g. 15,000h. 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 costs include both variable costs (the cost of producing each unit of product X and Y) and fixed costs ($90,000).
Given that each unit of product X contributes 4, and that twice as many units of product Y are sold as product X, we can express the total revenue as follows:
Total Revenue = 4(2X) = 8X = $18X
Where X is the number of units of product X sold.
The profit goal is 90,000. So, we can set up the following equation to solve for X:
Profit = Total Revenue - Total Costs 18X - 135,000 = 135,000 / $18 X = 7,500 units of product X
Since twice as many units of product Y are sold, the total number of units sold is:
Total Units = X + 2X = 7,500 + 2(7,500) = 22,500 units
So, the company must sell 22,500 units in total to make a profit of $45,000. Therefore, the answer is (f) 22,500.
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