CP Math Word Problem!!

Question

Victor runs a small sandwich shop. He decides to start offering bags of chips to his customers. He finds a supplier where he can buy chips for $0.30 per bag. Victor needs to determine how much to charge for the chips at his shop. He does some research by talking to other nearby sandwich shop owners. The table below shows their sales per week for two different prices. (The values are: 150 bags sold, for $1.00 per bag, and 350 bags sold, for $0.50 per bag.) Victor believes that there is a linear relationship between the number of bags sold and the price. Victor wants to price the bags of chips so that he will maximize his profits. Determine the price Victor should charge for a bag of chips. Use the equation P(x)=R(x)-C(x), where P(x) represents profit, R(x) represents revenue, and C(x) represents cost. Each is a function of the number of bags of chips sold, x. Round your answer to the nearest nickel.

Answer 1

Hi Bon, use the equation, P(x) = R(x) - C(x) twice, once for the bags selling for $1.00 and once for bags selling for $.50.

 

Bags selling for $1.00:

 

P(x) = 150 * 1.00 - 150 * .30

 

P(x) = 150 - 45

 

P(x) = 105, or the profit from selling 150 bags at $1.00 is $105.

 

Bags selling for $.50:

 

P(x) = 350 + .50 - 350 * .30

 

P(x) = 175 - 105

 

P(x) = 70, or the profit from selling 350 bags at .$50 is $70.

 

It would appear, more money can be made by charging more for the bags of chips and selling less than charging less for the bags of chips and selling more.

 

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