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A grocery store chain needs to transport of 3000m^3 of refrigerated goods and 4000m^3 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 20m^3 and a non-refrigerated goods section of 40m^3, while each truck of type B has both sections of the same volume of 30m^3. 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?
Please answer within 10 min., I don't have much time.
+130511 A grocery store chain needs to transport of 3000m^3 of refrigerated goods and 4000m^3 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 20m^3 and a non-refrigerated goods section of 40m^3, while each truck of type B has both sections of the same volume of 30m^3. 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?
I think you must mean cost "per cubic meter" rather than cost "per kilometer."
Let x be the number of type A trucks needed and y be the number of type B trucks needed.
Here are the constraints
20x + 30y ≤ 3000
40x + 30y ≤ 4000
The total cost will be the number of each type of truck rented* the capacity of each * the cost per cubic meter....so....we have the following objective function, z, which we wish to minimze
z = x*60*30 + y*60*40
z = 1800x + 2400y
Here's the graph of the constraints : https://www.desmos.com/calculator/mr9doouggj
The minimum cost is realized at the corner point of the intersection of both inequalities......this happens at (50, 66.667) .......so you need 50 trucks of type A and 67 trucks of type B
And the minimum cost will be $270,000
