Suppose thatTip can write 4 pages of term papers or solve 4 workbook problems in an hour, while Spot can write 5 pages of term papers or solve 15 workbook problems in an hour.If they each decide to work a total of 6 hours and to share their output, then if they produce as many pages of term paper as possible given that they produce 20 workbook problems,
A)both students will spend some time at each task.
B)Spot will write term papers only and Tip will do workbook problems only.
C)Spot will spend all of his time writing term papers and Tip will spend some time at each task.
D)Tip will spend all of his time writing term papers and Spot will spend some time at each task.
E)Tip will write term papers only and Spot will do workbook problems only.

Question

Quizplus · Accepted Answer

Let x be the number of hours Tip spends on writing term papers, and y be the number of hours Spot spends on writing term papers.

From the problem, we know that:
4x + 5y = number of pages of term paper produced
4x + 15y = 20 (since they produce 20 workbook problems)

We want to maximize the number of pages of term paper produced, which means we want to maximize 4x + 5y.

To solve for x and y, we can use elimination. We can subtract the second equation from the first to eliminate x:
(4x + 5y) - (4x + 15y) = (y = number of pages of term paper produced - 5y)
-10y = number of pages of term paper produced - 20
y = 2 - 0.1(number of pages of term paper produced)

Now we can substitute this expression for y into either of the original equations to solve for x. Let's use the first equation:
4x + 5(2 - 0.1(number of pages of term paper produced)) = number of pages of term paper produced

Simplifying this equation, we get:
4x + 10 - 0.5(number of pages of term paper produced) = number of pages of term paper produced
4x + 10 = 1.5(number of pages of term paper produced)
x = (1.5(number of pages of term paper produced) - 10) / 4

Now we know x and y in terms of the number of pages of term paper produced. To maximize the number of pages produced, we want to find the value of the number of pages that gives the largest possible value of 4x + 5y.

Graphing this expression, we get a line with a slope of -4/5. The largest possible value occurs when the line intersects the feasible region, which is a triangle with vertices at (0, 0), (5/4, 0), and (0, 2). We can check each vertex to see which one gives the largest value of 4x + 5y.

At (0, 0), 4x + 5y = 0
At (5/4, 0), 4x + 5y = 4(5/4) + 5(0) = 5
At (0, 2), 4x + 5y = 4(0) + 5(2) = 10

Therefore, the largest possible value of 4x + 5y is 10, which occurs when Tip spends all of his time writing term papers and Spot spends some time on each task. Answer choice D is the correct answer.

Suppose ThatTip Can Write 4 Pages of Term Papers or Solve