SOLUTION: A Company manufactures two different products, A and B. Each unit of product A costs $6 to produce and each unit of product B costs $4. The Company insists that total costs for the

Question 1179365: A Company manufactures two different products, A and B. Each unit of product A costs $6 to produce and each unit of product B costs $4. The Company insists that total costs for the two products be $500.
(a) Define the cost equation which states that the total cost of producing x units of product A and y units of product B equals $500
(b) Assuming the Company has agreed to fill an order for 50 units of product A, how many units of product B should be produced if total costs are to be kept at $500?

Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Let's solve this problem step-by-step:
**(a) Define the Cost Equation:**
* Let 'x' represent the number of units of product A produced.
* Let 'y' represent the number of units of product B produced.
* The cost of producing 'x' units of product A is 6x.
* The cost of producing 'y' units of product B is 4y.
* The total cost is the sum of these costs, which must equal $500.
Therefore, the cost equation is:
**6x + 4y = 500**
**(b) Calculate the Number of Units of Product B:**
* We are given that x = 50.
* Substitute x = 50 into the cost equation:
* 6(50) + 4y = 500
* 300 + 4y = 500
* Solve for y:
* 4y = 500 - 300
* 4y = 200
* y = 200 / 4
* y = 50
**Answer:**
(a) The cost equation is 6x + 4y = 500.
(b) The company should produce 50 units of product B.

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