word problems
sweater15
wordproblmes_12.docx1. 1-22
St. Joseph’s School has 1,200 students, each of whom currently pays $8,000 per year to attend. In addition to revenues from tuition, the school receives an appropriation from the church to sustain its activity. The budget for the upcoming year is $15 million, and the church appropriation will be $4.8 million. By how much will the school have to raise tuition per student to keep from having a shortfall in the upcoming year?
2. 1-23
Refer to Problem 1-22. Sensing resistance to the idea of raising tuition from members of St. Joseph’s Church, one of the board members suggested that the 960 children of church members could pay $8,000 as usual. Children of nonmembers would pay more. What would the nonmember tuition per year be if St. Joseph’s wanted to continue to plan for a $15 million budget?
The owner of a private freighter is trying to decide which cargo he should carry on his next trip. He has two choices of cargo, which he can agree to carry in any combination. He may carry up to 15 tons of cargo A, which takes up 675 cubic feet per ton and earns revenue of $85 per ton. Or, he may carry up to 54 tons of cargo B, with a volume of 450 cubic feet per ton and revenue of $79 per ton.
The freighter is divided into two holds, starboard and port. The starboard hold has a volume of 14,000 cubic feet and a weight capacity of 26 tons. The port hold has a volume of 15,400 cubic feet and a weight capacity of 32 tons. For steering reasons, it is necessary that the weight be distributed equally between the two sides of the freighter. However, the freighter engines and captain’s bridge, which together weight 6 tons, are on the starboard side of the freighter. This means that the port side is usually loaded with 6 tons more cargo to equalize the weight. The owner may carry any combination of the two cargoes in the same hold without a problem. How should this freighter be loaded to maximize total revenue?
3-37
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A paint company has two types of bases from which it blends two types of paints: Tuffcoat and Satinwear. Each base has a certain proportion of ingredients X, Y, and Z, as shown in the table at the top of p. 114 , along with their costs. |
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Table for Problem 3-37
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Ingredient X |
Ingredient Y |
Ingredient Z |
Cost/Gallon |
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Paint base A |
25% |
34% |
10% |
$4.50 |
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Paint base B |
35% |
42% |
15% |
$6.50 |
The specifications for the two paints are shown in the following table.
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Tuffcoat |
Satinwear |
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Must contain at least 33% ingredient X |
Must contain at least 30% ingredient X |
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Must contain at least 35% ingredient Y |
Must contain at least 38% ingredient Y |
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Must contain no more than 14% ingredient Z |
Must contain no more than 13% ingredient Z |
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Demand = 1,600 gallons |
Demand = 1,250 gallons |
How should the two bases be blended to manufacture the two paints at a minimum cost? What is the cost per gallon for each paint?
