Answer to Question #320391 in Calculus for koi

Question

A retailer receives a shipment of 10,000 kilograms of rice that will be used up over a 5-month period at the constant rate of 2,000 kilograms per month. If storage costs are 1 cent per kilogram per month, how much will the retailer pay in storage costs over the next 5 months?

Answer 1

Solution;

Let x be the amount of rice being stored at a time t(in months)

The slope-intercept form is ;

$y=mx+b$

m is the slope and b is the y-intercept.

The retailer receives;

$x(0)=10,000$

The rice is used at a constant rate of 2000kg per months,hence;

$y=mx+b$

$10000=-2000(0)+b$

$b=10,000$

Hence the linear relation for the usage is

$y=10,000-2000x$

Over the period $0\leq x\leq5$

The cost of storage 1cent per kilogram per month;

This is $0.01

Multiply with the usage per month;

$y_c=0.01(10,000-2000x)$

$C=100-20x$

Total cost over 5 months is;

$C=\displaystyle\int_0^5(100-20x)dx$

$C=[100x-10x^2]_0^5$

$C=250$ dollars