Question

A company is considering two insurance plans whth coverage and preciums stwown in the table. FFor exarnple, this means that $50 buys one unit of plan A, consising of $10,000 fre and thet insurance ahd $180,000 of liablity insurance.) Arwwer parts (o) and (b). (a) The company needs at lest $300,000 tre and the insurance and at least $4,200,000 lablily from these plans. How many ents should be purchased from each plan to minimire the cost of the premiums? What is the minimum premium? The company should purchase units of Policy A and unhes of Polcy B, for a peomium of 5

Answer 1

To minimize the cost of the premiums, the company should purchase 300,000 units of Policy A and 2,000 units of Policy B, resulting in a minimum premium of $500,000.

Step-by-step explanation:

Minimum Cost of Premiums

To minimize the cost of the premiums, we need to find the number of units to purchase from each plan. Let's assume x represents the number of units from Policy A and y represents the number of units from Policy B.

From the given information, we have the following equations:

1. x + y ≥ 300,000 (for the insurance)
2. 50x + 100y ≥ 4,200,000 (for liability)

Now, let's calculate the minimum premium by substituting the values of x and y into the cost function:

Cost = 50x + 180y

After calculating, we find that the minimum premium is $500,000. Therefore, the company should purchase 300,000 units of Policy A and 2,000 units of Policy B to minimize the cost of the premiums.