Clarissa’s utility function is U(r, z) = z + 120r – r^2

| November 24, 2016

Clarissa’s utility function is U(r, z) = z + 120r – r^2, where r is the number of rose plants she has in her garden and z is the number of zinnias. She has 250 square feet to allocate to roses and zinnias. Roses each take up 4 square feet and zinnias each take up 1 square foot. She gets the plants for free from a generous friend. If she acquires another 100 square feet of land for her garden and her utility function remains unchanged, she will plant?

The answer is 100 more zinnias and no more roses.

Would appreciate help on how to determine how this answer was arrived at.

Thanks!

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