Question

a company is considering two insurance plans with coverage and premiums shown in the table. (for example, this means that $50 buys one unit of plan A, consisting of $10,000 fire and theft insurance and $180,000 of liability insurance.) Answer parts a and b.

table:
                      policy A.               Policy B.
Fire/theft     $10,000              $15,000
Liability         $180,000           $120,000
Premium       $50                     $40

a. The company needs at least $450,000 fire and theft insurance and at least $7,200,000 liability from these plans. How many units should be purchased from each plan to minimize the cost of the premiums? What is the minimum premium?

Answer 1

Let the company buys a unit of policy A and b unit of policy B

Hence, objective function is to minimize 50a + 40b subject to:

10,000a + 15,000b ≥ 450,000 --------------- (1)

and 180,000a + 120,000b ≥ 7,200,000 ----------(2)

(2) - 8 x (1) gives:

(180,000 - 8 x 10,000)a = 100,000a = 7,200,000 - 8 x 450,000 = 3,600,000

Hence, a = 3,600,000 / 100,000 = 36

and b = (450,000 - 10,000a) / 15,000 = (450,000 - 10,000 x 36) / 15,000 = 6

Hence, the company should buy a = 36 units of policy A and b = 6 units of policy B.

And the minimum premium = 50a + 40b = 50 x 36 + 40 x 6 = $ 2,040