Question

You are moving temporarily for an internship. After packing up your car, you have one more box of essentials, totaling $640 in value, that you bring to the Post Office to ship to your new address. You know that there is a 1 in 7 chance that the box will be jostled in transit, causing $400 worth of damage.The USPS offers you insurance on your package for 60 cents ($0.60) per dollar of protection. You can buy any amount of this insurance, positive or negative. Let cd and cnd represent the net value of the package (including damage, insurance payments, and claims) in the cases that it is damaged and not damaged, respectively. Which equation best characterizes the set of possible combinations of cd and cnd?

(a)cnd= 500−0.40cd (b)cnd= 1000−1.5cd (c)cnd= 100−0.60cd (d)cnd= 640−2.5cd

Can anyone help me solve this?

Answer 1

Let k be the amount of insurance brought.

In case of no damage

(640 is original value. 0.6 is the cost per dollar of insurance)

In case of damage

We need to compare C_d and C_nd. For this, we need to eliminate 'k' from the picture.

Rearranging,