Im dumb Please help me understand this A company is consider

I\'m dumb. Please help me understand this.

A company is considering two insurance plans with coverage and premiums shown in the table. (For example, this Policy A Policy B means that $50 buys one unit of plan A, consisting of $10,000 fire and theft insurance and $180,000 of liability Fire Theft $10,000 $15,000 insurance) Answer parts a and b Liability $180,000 S120,000 Premium $50 $40 a. The company needs at least $300.000 &e; and theft insurance and at least $4200,000 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? The company should purchase H units of Policy A and Li units of Policy B, for a premium of b, Suppose the premium for policy A is reduced to $25. Now how many units should be purchased from each plan to minimize the Cost of the premiums? What is the minimum premium? The company should purchase units of Policy A and [units of Policy B, for a premium of $

Solution

Say \'x\' units of A
And \'y\' units of B

10000x + 15000y >= 300000
Divide all over by 5000 :
2x + 3y >= 60

180000x + 120000y >= 4200000
Divide all over by 60000 :
3x + 2y >= 70

2x + 3y >= 60
3x + 2y >= 70

Graphing these :

Critical points are
a) (0 , 35)
b) (30 , 0)
c) (18 , 8)

To be minimized :

50x + 40y

For (0,35) :
50(0) + 40(35) = 1400

For (30 , 0) :
50(30) + 40(0) =1500

For (18 , 8) :
50(18) + 40(8) = 1220 ---> minimum

So, company should purchase 18 units of policy A and 8 units of policy B,
for a premium of $1220

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b)

25x + 40y

For (0,35) :
25(0) + 40(35) = 1400

For (30 , 0) :
25(30) + 40(0) = 750

For (18 , 8) :
25(18) + 40(8) = 770

The company should purchase 30 units of policy A and 0 units of policy B for a premium of $750