Optimization: fuel expenses of truck on flat interstate

[parsons9]

I'm okay at story problems, but I don't get this one.

"A truck driving over a flat interstate at a constant speed of 50 mph gets 4 miles to the gallon. Fuel costs $1.19 per gallon. The truck loses a tenth of a mile per gallon in fuel efficiency for each mile per hour increase in speed. Drivers are paid $27.50 per hour in wages and benefits. Fixed costs for running the truck are $11.33 per hour. A trip of 300 miles is planned. What speed minimizes operating expenses?"

I know that (cost=fuel + wages + truck expenses) and (distance=rate x time), but I can't figure out what to do with those.

 

[mmm4444bot]

Let x = the number of 1-mph increases above 50 mph

EGs

When x = 1, then trip speed is 51 mph.

When x = 8, then trip speed is 58 mph.

When x = 12, then trip speed is 62 mph.

Use the expression 50 + x as the speed.

From this, and the distance of 300 miles, find the time.

Use the time to calculate the wages and fixed costs.

The miles-per-gallon is a linear function of x, as well.

Use it to calculate the fuel cost.

Add it all together.

If you need more help, then please show your work, so far, and try to say something about why you're unsure or stuck.