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quester [9]
2 years ago
11

A movie theater manager of a small theater sells two sizes of popcorn at the concession stand. A jumbo popcorn has a profit of $

4 and a mini popcorn has a profit of $3. The manager knows the maximum number of popcorn boxes that will fit in the concession stand, the cost of making the popcorn, and the minimum number of boxes he wants to sell each day. Let j represent the number of jumbo popcorns sold and let m represent the number of mini popcorns sold. What is the objective function, and how can it be used to maximize the profit based on the the given conditions?
Mathematics
1 answer:
NeX [460]2 years ago
5 0

j4 + m3 = p

If you multiply j, which is the number of jumbo popcorns sold by its price, you are given the profit of the Jumbo boxes for a single day. If you multiply m, which is the number of mini popcorns sold by its price, you are given the profit of the Mini boxes for a single day. If you add the profits from both boxes together... you are given p, which is the total profit for the day.

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Please help me out :P
Veseljchak [2.6K]

cos θ = \frac{-4\sqrt{65} }{65}, sin θ = \frac{-7\sqrt{65} }{65}, cot  θ  = 4/7, sec  θ = \frac{-\sqrt{65} }{4}, cosec  θ  = \frac{-\sqrt{65} }{7}

<h3>What are trigonometric ratios?</h3>

Trigonometric Ratios are values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Sin θ: Opposite Side to θ/Hypotenuse

Tan θ: Opposite Side/Adjacent Side & Sin θ/Cos

Cos θ: Adjacent Side to θ/Hypotenuse

Sec θ: Hypotenuse/Adjacent Side & 1/cos θ

Analysis:

tan θ = opposite/adjacent = 7/4

opposite = 7, adjacent = 4.

we now look for the hypotenuse of the right angled triangle

hypotenuse = \sqrt{7^{2} + 4^{2} } = \sqrt{49+16} = \sqrt{65}

sin θ = opposite/ hyp = \frac{7}{\sqrt{65} }

Rationalize, \frac{7}{\sqrt{65} } x \frac{\sqrt{65} }{\sqrt{65} } = \frac{7\sqrt{65} }{65}

But θ is in the third quadrant(180 - 270) and in the third quadrant only tan and cot are positive others are negative.

Therefore, sin θ = - \frac{7\sqrt{65} }{65}

cos   θ  = adj/hyp = \frac{4}{\sqrt{65} }

By rationalizing and knowing that cos  θ  is negative, cos θ  = -\frac{-4\sqrt{65} }{65}

cot θ  = 1/tan θ  = 1/7/4 = 4/7

sec θ  = 1/cos θ  = 1/\frac{4}{\sqrt{65} } = -\frac{-\sqrt{65} }{4}

cosec θ  = 1/sin θ  = 1/\frac{\sqrt{65} }{7} = \frac{-\sqrt{65} }{7}

Learn more about trigonometric ratios: brainly.com/question/24349828

#SPJ1

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Answer:

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Step-by-step explanation:

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