Question

The Hits on a Shoestring music company is trying to plan its next month’s work. The company makes CDs of both rock and rap groups. It costs them an average of $1200 to produce a rap CD and $1500 to produce a rock CD (more instrumentalists). It takes about 18 hours to produce a rock CD and about 25 hours for a rap CD. The company can afford to spend up to

The Hits on a Shoestring music company is trying to plan its next month’s work. The company makes CDs of both rock and rap groups. It costs them an average of $1200 to produce a rap CD and $1500 to produce a rock CD (more instrumentalists). It takes about 18 hours to produce a rock CD and about 25 hours for a rap CD. The company can afford to spend up to $15,000 on production next month. Also, according to an
agreement with the employee union,the company must spend at least 175 hours on production. If the company makes $20,000 in profit on each rock CD they produce and $30,000 in profit on each rap CD they produce, how many of each should they produce to maximize their profit?
A) Write an inequality to solve the problem
B) Graph, shade the region of feasible solutions.

Answer 1

To maximize profit, the Hits on a Shoestring music company should set up a system of inequalities and graph the feasible region to determine the number of rock CDs and rap CDs to produce.

Step-by-step explanation:

To determine the number of rock CDs and rap CDs that the Hits on a Shoestring music company should produce to maximize their profit, we can set up a system of inequalities based on the given information. Let's denote the number of rock CDs as 'x' and the number of rap CDs as 'y'.

The cost constraint can be expressed as: 1500x + 1200y <= 15000

The labor hour constraint can be expressed as: 18x + 25y >= 175

The profit can be calculated using the equation: Profit = 20000x + 30000y

To graph the feasible region, we need to graph the inequalities and shade the region that satisfies all the constraints. The feasible region will be the intersection of the shaded regions. From this region, we can determine the values of 'x' and 'y' that will maximize the profit.