Karla wants to grow spinach. 1 pound of Fertilizer(F) produces 20 spinach or 1 p

Question

Karla wants to grow spinach. 1 pound of Fertilizer(F) produces 20 spinach or 1 pound of Manure(M) produces 30 spinach. They are perfect substitutes. So we know Q=20F+30M

Now Karla wants to produce 300 spinach at the least possible cost given that:
1 pound of Fertilizer costs $5 and 1 pound of Manure costs $10.

Please explain to me how to minimize the cost.

C($5,$10,300spinach)=???

Explanation / Answer

Q=20F+30M cost = 5F+10M now minimizing cost we have Q = 300 = 20F+30M =>30=2F +3M F=(30-3M)/2 now, putting it in cost equation we get cost = 10M+ 5((30-3M)/2) => 10m + 45 -7.5M = 45 +2.5M this is minimum for M = 0 M=0 F = 15 cost = 15x5 =$ 75

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