John owns a house painting company. an experienced crew can prep 6 rooms and paint 2 rooms in a week. a novice crew can prep 2 rooms and paint 2 rooms in a week. an experienced crew gets paid $1000 per week and a novice crew gets paid $750 per week. to stay on schedule, john needs at least 12 rooms prepped and 8 rooms painted per day. how many weeks should each crew be scheduled to minimize cost?

Let number of experienced crew = X Let number of novice crew = Y Number of rooms experienced crew can prep = 6X Number of rooms experienced crew can paint = 2X Number of rooms novice crew can prep = 2Y Number of rooms novice crew can paint = 2Y Number of rooms to be prepped per week = 12 Number of rooms to be painted per week = 8 So, we have Equation 1 - For Prepping 6X + 2Y = 12 Equation 2 - For Painting 2X + 2Y = 8 or 2Y = 8 - 2X Replacing the value of 2Y from equation 2 in equation 1, we have 6X + (8 - 2X) = 12 Simplifying the equation we get 4X + 8 = 12 4X = 12 -8 4X = 4 X = 4/4 X = 1 Replacing the value of X in Equation 1, we get 6 * 1 + 2Y = 12 2Y = 12 - 6 2Y = 6 Y = 6/2 Y = 3 Total cost per week = 1 * 1000 + 3 * 750 = 1000 + 2250 = 3250 So, to optimize costs, John would need 1 experienced crew and 3 novice crews at a total cost of $3250 per week.

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