
Resource Allocation Arctic Juice Company makes three juice blends: PineOrange, using 2 portions of pineapple juice and 2 portion of orange juice per gallon; PineKiwi, using 3 portion of pineapple juice and 1 portion of kiwi juice per gallon: and OrangeKiwi, using 3 portions of orange juice and 1 portion of kiwi juice per gallon. Each day the company has 800 portions of pineapple juice, 650 portions of orange juice, and 350 portions of kiwi juice available. Its profit on PineOrange is $1 per gallon, it profit on PineKiwi is $2 per gallon, and its profit on OrangeKiwi is $1 per gallon. How many gallon of each blend should it make each day to maximize profit? What is the largest possible profit the company can make?

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Chapter 5 Solutions
Finite Mathematics, Loose-leaf Version
- No chatgpt pls will upvotearrow_forward(7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz). Ꮖ (a) (4 points) Show that V x F = 0. (b) (4 points) Find a potential f for the vector field F. (c) (4 points) Let S be a surface in R3 for which the Stokes' Theorem is valid. Use Stokes' Theorem to calculate the line integral Jos F.ds; as denotes the boundary of S. Explain your answer.arrow_forward(3) (16 points) Consider z = uv, u = x+y, v=x-y. (a) (4 points) Express z in the form z = fog where g: R² R² and f: R² → R. (b) (4 points) Use the chain rule to calculate Vz = (2, 2). Show all intermediate steps otherwise no credit. (c) (4 points) Let S be the surface parametrized by T(x, y) = (x, y, ƒ (g(x, y)) (x, y) = R². Give a parametric description of the tangent plane to S at the point p = T(x, y). (d) (4 points) Calculate the second Taylor polynomial Q(x, y) (i.e. the quadratic approximation) of F = (fog) at a point (a, b). Verify that Q(x,y) F(a+x,b+y). =arrow_forward
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