Tina\'s Material Company hauls gravel to a construction site, using a small truc

Question

Tina's Material Company hauls gravel to a construction site, using a small truck and a large truck. The carrying capacity and operating cost per load are given in the accompanying table. Tina must deliver a minimum of 200 cubic yards per day to satisfy her contract with the builder. The union contract with her drivers requires that the total number of loads per day is a minimum of 6. How many loads should be made in each truck per day to minimize the total cost?

In order to minimize the total cost, the number of loads in a small truck that should be made is __ and the number of loads in a large truck that should be made is __.

Explanation / Answer

Lets take the variables :

x = small truck T= Total cubic yards

y= large truck C = Cost

A small truck can hold 40 cubic yards and large truck can hold 50 cubic yards

Total cubic yards T = 40x + 50y

There must be a minimum of 6 loads

Any Combinations of 6 small or large trucks will meet the required minimum of 200 yards

For example, 6 small trucks and o large trucks

T = 40x + 50y

= 40 * 6 + 50 * 0

T = 240

At other extreme, 0 small trucks and 6 large trucks

T = 40x + 50y

T = 40*0 + 50*6

T =300

Therefore we have only to concern ourselves with minimizing the cost.

Cost per load of small truck is $63 and for large truck is $54

Therefore, cost = 63x + 54y

Calculate the cost of each possible combination using the above cost formula

( 0,6) 63 *0 + 54*6 = $324

( 1, 5) 63*1 + 54*5 = $ 333

( 2, 4) 63*2 + 54*4 = $ 342

( 3, 3) 63*3 + 54*3 = $ 351

We can see the pattern. The more the small trucks are used, the higher the cost. There fore, the most cost effective option would be to use 6 large trucks. This would provide 50*6 = 300 cubic yards and would cost 54*6 = $324

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