Of the given situation, we have to frame a system of inequalities and also graph it showing feasible region and coordinates. Also, we have to write a profit function for selling the number cookies and muffins and finally, calculate the maximum profit from it.
Answer to Problem 13STP
(a) The inequalities are:
(c) Profit function = $12 x + $8 y
(d) maximumprofit = $ 92
Explanation of Solution
Given Information
ingredients for each tray of cookies = 5 cups of flour + 2 cups of sugar
ingredients for each tray of muffins = 5 cups of flour + 1 cups of sugar
Total number of cups of flour available = 40
Total number of cups of sugar available = 15
Profit per tray of cookies = $ 12
Profit per tray of muffins = $ 8
Calculation (a)
Let,
x = number of trays of cookies baked
y = number of trays of muffins baked
So, according to the data’s given,
(b) Solving equation (iii) and (iv) to intercept form, that is,
where ‘ a’ and ‘ b’ will be ‘ x’ and ‘ y’ intercept respectively.
from (iii), we have
⇒
⇒
from (iv), we have
⇒
Graph
Plotting these on the graph, we get,
co-ordinates of vertices in feasible region,
A = (0, 8)
B =
P = (7, 1)
(c) Profit function = $ 12x + $ 8y
(d) Maximum profit
For maximum profit, Tonya should sell, 7 trays of cookies and 1 tray of muffins
Therefore, maximum profit = ($ 12 × 7) + ($ 8 × 1)
= $ 84 + $ 8
= $ 92
Chapter 3 Solutions
Glencoe Algebra 2 Student Edition C2014
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