For the $6-$inch$-$thick slab under your new ${30}^{\text{'}\text{'}}$ x ${180}^{\text{'}}$ equipment barn, you chose to use a $4000-$ psi$-$rated concrete mix that calls for $600$ pounds of cement per cubic yard of poured concrete.

For mixer truck delivery of mixed concrete, you can order the small truck at $$120/$ cu$.$yd $+$$$120$ service fee per trip$)$ or the big truck $(40,000lbs$ per load $at$ $$100$ per $cuyd+$ $$400$ service fee per trip

Concrete weighs about $150$ pounds per cubic foot.

a$.$ To help plan for soil compaction and grading, how much will this slab weigh $($Lb$),$ and also per square foot $(lb$ per $f{t}^2)?$

b$.$ Disregarding the volume of any steel reinforcement you decide to include, how many pounds of cement do you need?