MA 162 Word Problem-3

Question

A company is considering two insurance plans with coverage and premiums.

Policy A:

Fire/Theft: $22,000

Liability: $184,000

Premium: $75

Policy B:

Fire/Theft: $34,000

Liability: $133,000

Premium: $57

A. The company needs at least $738,000 fire and theft insurance and at least $4,356,000 liability from these plans. How many units should be purchased from each plan to minimize the cost of premiums? What is the minimum premium?

The company should purchase_____units of Policy A and ____units of Policy B, for a premium of $____

Answer 1

suppose x units of plan A and y of Plan B are purchased

Then Fire / Theft insurance purchased (in $ 000s) is 22x + 34y > 738 region A

Liability : 184x + 133 y > 4356 region B

and cost of the policies : 75x + 57y ($)

Plot regions A and B on Desmos and look at the vertex of the overlapping regions (15,12)

So optimal position is x=15, y=12 with a cost of 75 x 15 + 57 x 12 = $ 1809