Podunk Insititute of Technology's Math Department offers two courses: Finite Math and Applied Calculus.Each section of Finite Math has 60 students, and each section of Applied Calculus has 50. The Department is allowed to offer a total of up to 110 sections. Furthermore, no more than 6,000 students want to take a math course. (No student will take more than one math course.) Sppose the university makes a profit of $100,000 on each section of Finite Math and $50,000 on each section of Applied Calculus. How many sections of each course should the department offer to make the largest profit?

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Asked Dec 2, 2019
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Podunk Insititute of Technology's Math Department offers two courses: Finite Math and Applied Calculus.Each section of Finite Math has 60 students, and each section of Applied Calculus has 50. The Department is allowed to offer a total of up to 110 sections. Furthermore, no more than 6,000 students want to take a math course. (No student will take more than one math course.) Sppose the university makes a profit of $100,000 on each section of Finite Math and $50,000 on each section of Applied Calculus. How many sections of each course should the department offer to make the largest profit?

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Expert Answer

Step 1

Let x and y denotes the number of sections of finite math and applied calculus. Then given problem can be formulated as,

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finite math applied calculus total sections 1 110 Students 60 6000 50 Profits 100000 50000 Z

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Step 2

That is,

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Maximizez 100000x + 50000 y Subject to x+y110 60x 50y6000 x, y 20

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Step 3

Sketch the region as...

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150 D(0,110)60x+ 50y= 6000 100 C(50,60) 50 ry110 B(100,0 100 4(0,0) -50 150 50 -50t

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