A factory sells backpacks for $40.00 each. The cost to make 1 backpack is $10.00. In addition to the costs of making backpacks, the factory has operating expenses of $12,000 per week. The factory's goal is to make a profit of at least $980 each week. Which inequality represents the number of backpacks, x, that need to be sold each week for the factory to meet thls goal? How many backpacks must the factory sell to meet its weekly goal? Select the inequality that represents this situation and select the correct statement. The factory must sell a minimum of 368 backpacks to meet the weekly goal. 30x+12,000=980 The factory must sell a minimum of 432 backpacks to meet the weekly goal. 30x−12,000=980 30x−12,000

Question

A factory sells backpacks for $40.00 each. The cost to make 1 backpack is $10.00. In addition to the costs of making backpacks, the factory has operating expenses of $12,000 per week. The factory's goal is to make a profit of at least $980 each week. Which inequality represents the number of backpacks, x, that need to be sold each week for the factory to meet thls goal? How many backpacks must the factory sell to meet its weekly goal? Select the inequality that represents this situation and select the correct statement. The factory must sell a minimum of 368 backpacks to meet the weekly goal. 30x+12,000>=980 The factory must sell a minimum of 432 backpacks to meet the weekly goal. 30x−12,000>=980 30x−12,000<=980 The factory must sell a minimum of 367 backpacks to meet the weekly goal. 30x+12,000<=980 The factory must sell a minimum of 433 backpacks to meet the weekly goal.

Bytelearn · Accepted Answer

Calculate Profit Per Backpack:  Calculate the profit per backpack sold. Subtract the cost of making one backpack from the selling price. Set Up Inequality:  Set up the inequality to find the minimum number of backpacks, x, needed to cover the operating expenses and achieve the weekly profit goal. Solve for x:  Solve the inequality for x. Isolate x:  Divide both sides by 30 to isolate x. Round Up to Nearest Whole Number:  Since x represents the number of backpacks, and it cannot be a fraction, round up to the nearest whole number.

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