polynomial arithmetic applications

Question

The Burke family has a donut store. It costs $5 for every dozen glazed donuts they make and $8.50 for every dozen maple donuts they make. Let g= number of dozen glazed and m= number of maple they make.

1) Write the equation for the total cost for the donuts.

2) If they sell a dozen glazed donuts for $8.00 and a dozen maple for $10.00 write the revenue equation: revenue= price*quantity.

3) Use the previous answers to write the profit equation and simplify.

4) The number of donuts they can make is limited to the available space. The total number of dozen donuts they can make is 120. Write an equation for the number of dozen glazed donuts in terms of the maple donuts (the equation should look like g=? with m in the right hand expression)

5) Substitute the value you found for g above into the profit equation and simplify it to obtain a polynomial equation with just m as the variable.

Answer 1

1) Cost = 5g + 8.5m

 

2) Revenue = 8g + 10m

 

3) Profit = Revenue - Cost

    Profit = 8g + 10m - (5g + 8.5m)

    Profit = 8g + 10m - 5g - 8.5m

    Profit = 3g + 1.5m

 

4) g + m = 120

    g = 120 - m

 

5) Profit = 3(120 - m) + 1.5m

    Profit = 360 - 3m +1.5m

    Profit = 360 - 1.5m

Answer 2

C=5g+8.50m

r=8g+10m

g+m=120

g=120-m

p=r-c

p=3g +1.50m

p=3(120-m)+1.5m=360-1.5m

 

what this says is if you make only glaze you maximize your profit at $360 dollars. Every maple dozen you make reduces your profit by $1.50.