How Many Units Must Plant A Produce to Stay Within Budget?

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The company plans to produce 5,000 units at plants A and B, with unit costs of $2.50 and $3.00, respectively. Fixed costs are $6,000 for plant A and $8,000 for plant B, with a total budget cap of $28,000. The equations set up include the total units produced and the cost equations for both plants. By substituting the number of units produced at plant B into the total cost equation, the minimum number of units that must be produced at plant A can be determined. The discussion focuses on confirming the calculations to ensure budget compliance.
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Homework Statement



A company will manufacture a total of 5000 units of its product at plants A and B. At plan A the unit cost for labor and material combined is 2.50 $, while at plant B it is 3.00 $. The fixed costs at plant A are 6000 $ and at plant B they are 8000 $. Between the two plants the company has decided to allot no more than 28,000 $ for total costs. What is the minimum number of units that must be produced at plant A ?





The Attempt at a Solution



I want to confirm my steps if it's right ,,,,

A = # units produced at plant A
B = # units produced at plant B

A + B = 5000
B = 5000 - A

Cost for plant A: 2.50A + 6000
Cost for plant B: 3.00B + 8000

(2.5A + 6000) + (3.0B + 8000) = 28000
 
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You already know that B = 5000 - A. Replace this value in the last equation.
 
kk ,,,,

i forgot to say it ,,, i
 

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