PLS HELP
A grocery store chain needs to transport of 3000m3 of refrigerated goods and 4000m3 of non-refrigerated goods. They plan to hire truck from a company that has two types of trucks for rent. A truck of type A has a refrigerated goods section of 20m3 and a non-refrigerated goods section of 40m3, while each truck of type B has both sections of the same volume of 30m3. The cost per kilometer of a Type A is $30, and $40 for Type B. How many trucks of each type should the grocer rent to achieve the minimum total cost?
Answers
Given : A grocery store chain needs to transport of 3000m³of refrigerated goods and 4000m³ of non-refrigerated goods. There are two types of trucks A & B .
To find : How many trucks of each type should the grocer rent to achieve the minimum total cost
Solution:
Refrigerated good R = 3000 m³
Non - Refrigerated good N = 4000 m³
Let say number of Truck type A = A
a refrigerated goods section of 20m³ and a non-refrigerated goods section of 40m³
Let say number of Truck type B = B
a refrigerated goods section of 30m³ and a non-refrigerated goods section of 30m³
20A + 30B ≥ 3000
40A + 30B ≥ 4000
Cost = 30A + 4B
From Graph Cost 30A + 40B
A = 0 B = 134 0 + 40 * 134 = 5360
A = 50 B = 67 30*50 + 40 * 67 = 4180
A = 51 B = 66 30*51 + 40 * 66 = 4170
A = 100 B = 34 30* 100 + 40 * 34 = 4360
Hence minimum Cost = 4170
51 A types Truck & 66 B type Trucks
Verification :
Refrigerated capacity = 20 * 51 + 30 * 66 = 3000
Non - Refrigerated Capacity = 40*51 + 30*66 = 4020 > 4000
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