Do the question below with deep explanation?

8. A dedicated XYZ family uses tomatoes and sugar to produce ketchup at home.
The quality of the ketchup (using a Bostwick consistometer) is a function of the
composition of the inputs. In particular, where K is the ketchup quality, T is the
availability of tomato in KG, and S is the availability of sugar in KG as an input for
ketchup production. Notice that both tomatoes and sugar are essential for ketchup
production, and that ketchup quality increases with the amount of either, but at a
decreasing rate. The price of tomatoes in the market is 50 ETB, while the price of
sugar is 5 ETB. The budget for this homemade ketchup is 5000. How many KG of
tomatoes and sugar will the XYZ family choose to maximize quality subject to this
budget constraint?
?(?, ?) = ?
0.2?
0.4
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