Math Equations: CD Production
It costs the company an average of $15,000 to produce a rock CD and an average of $12,000 to produce a rap CD. Also, it takes about 18 hours to produce a rock CD and about 25 hours to produce a rap CD. The company can afford to spend up to $150,000 on production next month. Also, the company will spend at least 175 hours on production. The company earns $20,000 in profit on each rock CD it produces and $30,000 in profit on each rap CD it produces. But the company recently promised its distributor that it would not release more rap music than rock.
The company needs to decide how many of each type of CD to make. Note: It can make a fraction of a CD next month and finish it the next month after. Graph the feasible region.
- a. Find at least three combinations of rock and rap CDs that would give the company a profit of $120,000, and mark these points in one color on your graph. The combinations do not have to be in the feasible region. )
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Profit - x20,000+y30,000 x=6, y=0 x=0, y=4 x=3, y=2.
- b. In a different color, mark points on your graph that will earn $240,000 in profits.
x=12, y=0 x=0, y=8 x=9, y=2 x=3, y=6 x=6, y=4
Find out how many CDs the company should make of each type next month to maximize its profit. It should make 5 and five-ninths of each CD to maximize profit. I know this because this is the highest point in the feasible region. Explain how you found an answer to Question 3 and why you think your answer gives the maximum profit.
I know this because this is the highest point in the feasible region. It’s hard to tell exactly just by graphing so the problem must be solved algebraically. I know that the lines “x=y” and “15,000x+12,000y-150,000” intersect at the highest point of the feasible region. Because x is equal to y, both coordinates must be the same. I inserted 3 different coordinates for both x and y and got that the coordinates (5. 6,5. 6) will give me the greatest profit that is closest to 150,000. A Rock ‘n’ Rap Variation Suppose the conditions were the same as in homework 12 except that the profits were reversed.
In other words, suppose the company made a $30,000 profit on each rock CD and $20,000 profit on each rap CD.
Profit: 30,000x+20,000y.
Would this change your advice to the company about how many CDs of each type to produce to maximize its profit? If so, how many of each type should the company make, and what would be the profit? Explain your answer. My answer would stay the same because x will still be equal to y, and the money available to spend won’t change. Since these are the only two lines that are taken into account, my advice would stay constant.
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