Question 1178936: 2.A firm produces headphone in two qualities, Basic (B) and Premium (P). For the coming year, the estimated output of B is 50% higher than that of P. The profit per unit sold is $300 for P and $200 for B. If the profit target is $180 000 over the next year, how much of each of the two qualities must be produced?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! b = number of basic headphones
p = number of premium headphones.
profit for basic = 200 each.
profit for premium = 300 each.
number of basic headphones made is 1.5 times the number of premium headphones made.
total profit target is 180,000.
you have two equations that need to be solved simultaneously.
they are:
b = 1.5 * p
200 * b + 300 * p = 180,000
in the second equation, replace b with 1.5 * p to get:
200 * (1.5 * p) + 300 * p = 180,000
simplify to get:
300 * p + 300 * p = 180,000
combine like terms to get:
600 * p = 180,000
solve for p to get:
p = 180,000 / 600 = 300
since b = 1.5 * p, then b = 1.5 * 300 = 450.
450 * 200 profit for basic headphone plus + 300 * 300 profit for premium headphone = 180,000 total profit.
1.5 * 300 premium headphones = 450 basic headphones.
the basic requirements of the problem are satisfied.
the solution is that the firm needs to produce and sell 450 basic headphones and 300 premium headphones to make a profit of 180,000,
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