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Sagot :
The optimal number of pots and plates Josh should make is given from
the graph of the inequalities.
Response:
a. 2·p + a ≤ 50
p ≤ 24
a ≤ 40
b. The coordinates of the vertices of the feasible region are; (24, 2), (40, 5), (0, 40), (24, 0), (0, 0)
c. 40 pots and 5 plates
How can the optimal number of plates and pots Josh should make be found?
Given:
Number of days Josh has to make pots and plates to sell = 8 days
Weight of each pot = 2 pounds
Weight of each plate = 1 pound
Weight Josh cannot carry = More than 50 pounds
Number plates he can make each da = At most 5 plates
Number of pots he can make each day = At most 5 pots
The profit Josh makes for each plate sold = $12
Profit from each pot sold = $25
a. Let p represent the number of pots Josh makes and let a represent the
number plates. The linear inequalities are;
2·p + a ≤ 50
p ≤ 8 × 3 = 24
p ≤ 24
a ≤ 5 × 8 = 40
a ≤ 40
b. When p = 24, we have;
2 × 24 + a = 50
a = 2
When a = 40, 2·p + 40 = 50, gives;
p = 5
The vertex points are;
The coordinates of the vertices of the feasible region are;
(24, 2), (40, 5), (0, 40), (24, 0), (0, 0)
c. The profit function is; P = 25·p + 12·a
The profit at the vertices are;
[tex]\begin{tabular}{|c|c|c|}p&a&Profit\\0&0&0\\0&40&12 \times 40 = 480\\24&0&25 \times 24 = 600\\24&2&12 \times 2 + 25 \times 40 = 624\\40&5&12 \times 5 + 25 \times 40 = 660\end{array}\right][/tex]
To maximize his potential profit, therefore;
- Josh should make 40 pots and 5 plates.
Learn more about linear optimization here:
https://brainly.com/question/15356519
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