Word Problem-4

Question

A company is considering two insurance plans with coverage and premiums.
Policy A:
Fire/Theft: $10,000
Liability: $180,000
Premium: $50

Policy B:
Fire/Theft: $15,000
Liability: $120,000
Premium: $40

A. The company needs at least $450,000 fire and theft insurance and at least %4,800,000 liability from these plans. How many units should be purchased from each plan to maximize 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

Say, units purchased for policy A = x

        units purchased for policy B = y

 

So, as per data given---

 

10000x+15000y<=450000

180000x+120000y<=4800000

 

On simplifying---

 

2x+3y<=90

3x+2y<=80

 

Once we graph the inequalities---

 

the extreme points are (0,30),  (27,0),   (12,22)

 

The objective function is (50x +40y)

 

Value of objective function at the various extreme points---

(0,30)-------30*40=1200

(27,0)-------27*50=1350

(12,22)-----12*50+22*40=1480--------optimal point

 

So the company must choose 12 units of policy A & 22 units of policy B

For a premium of 1480 $